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After applying an arithmetic operation to two operands and getting a result, you can use this procedure to improve your confidence that the result is correct.
Sum the digits of the first operand; any 9s (or sets of digits that add to 9) can be counted as 0.
If the resulting sum has two or more digits, sum those digits as in step one; repeat this step until the resulting sum has only one digit.
Repeat steps one and two with the second operand. You now have two one-digit numbers, one condensed from the first operand and the other condensed from the second operand. (These one-digit numbers are also the remainders you would end up with if you divided the original operands by 9; mathematically speaking, they're the original operands modulo 9.)
Apply the originally specified operation to the two condensed operands, and then apply the summing-of-digits procedure to the result of the operation.
Sum the digits of the result you originally obtained for the original calculation..
If the result of step 4 does not equal the result of step 5, then the original answer is wrong. If the two results match, then the original answer may be right, though it isn't guaranteed to be. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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In mathematics, physics, and engineering, a Euclidean vector (sometimes called a geometric or spatial vector, or—as here—simply a vector) is a geometric object that has magnitude (or length) and direction and can be added to other vectors according to vector algebra. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Check out Ebook "Mind Math" from Dr. Garg
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Check out Ebook "Mind Math" from Dr. Garg
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Let’s look at the fascinating RAND function. This intriguing and useful function returns a Random Number that is Greater Than or Equal to 0 and Less Than 1. Each time your worksheet recalculates, (by reopening or forced recalculation by pressing F9), the RAND function returns a New Random Number.
It should be noted that some hard core statisticians have voiced concerns about the true Randomness of the RAND function (it is prone to sequential correlations if large runs of numbers are taken), but it suffices for nearly all but the most demanding statistical applications, and if fine for us mere mortals.
The Syntax for the Rand function is simply:
RAND( )
If you want to create a random number between two numbers, (where a is the smallest number and b is the largest number), you can use the following:
=RAND()*(b-a)+a
If you want only Whole Numbers you can use:
RANDBETWEEN()
For example, =RANDBETWEEN(1, 500) will produce a Random Whole Number between 1 and 500.
There are countless statistical applications, of course, but you can also use it in some entertaining applications. For example, some Excel Enthusiasts have used it to create Tetris-style and Dice-Rolling games in Excel.
I have used the RAND function in conjunction with other functions and graphics to create a Slot Machine in Excel (send me a request at [email protected] if you would like a copy of the Slot Machine spreadsheet). I will be happy to send a copy to you.
The RAND function. Great for use in statistical applications, building games, slot machines, and other Fun Stuff!
Wheel Of Karma by Audionautix is licensed under a Creative Commons Attribution license (https://creativecommons.org/licenses/by/4.0/)
Artist: http://audionautix.com/ http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Imagine a circular dartboard of radius 1 foot mounted on a square backdrop of side 2 feet. Now suppose darts are thrown. Of the darts that land within the square, some will land inside the circle of the dartboard (hits) and others will lie outside the circle but inside the square. Imagine the dartboard centered on a cartesian grid with its center at (0,0). Select two floating point numbers x and y both in the range from -1.0 to 1.0. (x,y) are the coordinates of a dart randomly thrown that lands within the square. Sometimes, the dart will also be within the circle. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Welcome to Garg University!!
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Monte Carlo methods are used in finance and mathematical finance to value and analyze (complex) instruments, portfolios and investments by simulating the various sources of uncertainty affecting their value, and then determining their average value over the range of resultant outcomes. This is usually done by help of stochastic asset models. The advantage of Monte Carlo methods over other techniques increases as the dimensions (sources of uncertainty) of the problem increase.
Monte Carlo methods were first introduced to finance in 1964 by David B. Hertz through his Harvard Business Review article, discussing their application in Corporate Finance. In 1977, Phelim Boyle pioneered the use of simulation in derivative valuation in his seminal Journal of Financial Economics paper.
This article discusses typical financial problems in which Monte Carlo methods are used. It also touches on the use of so-called "quasi-random" methods such as the use of Sobol sequences. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Home equity is the market value of a homeowner's unencumbered interest in their real property—that is, the difference between the home's fair market value and the outstanding balance of all liens on the property. The property's equity increases as the debtor makes payments against the mortgage balance, and/or as the property value appreciates. In economics, home equity is sometimes called real property value.
Technically, home equity has a zero rate of return and is not liquid. Home equity management refers to the process of using equity extraction via loans—at favorable, and often tax-favored, interest rates—to invest otherwise illiquid equity in a target that offers higher returns.
Homeowners acquire equity in their home from two sources. They purchase equity with their down payment, and the principal portion of any payments they make against their mortgage. They also benefit from a gain in equity when the value of the property increases. Investors typically look to purchase properties that will grow in value, causing the equity in the property to increase, thus providing a return on their investment when the property is sold.
Home equity may serve as collateral for a home equity loan or home equity line of credit (HELOC). Many home equity plans set a fixed period during which the person can borrow money, such as 10 years. At the end of this "draw period," the person may be allowed to renew the credit line. If the plan does not allow renewals, the person will not be able to borrow additional money once the period has ended. Some plans may call for payment in full of any outstanding balance at the end of the period. Others may allow repayment over a fixed period, for example, 10 years. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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In financial accounting, a balance sheet or statement of financial position is a summary of the financial balances of a sole proprietorship, a business partnership, a corporation or other business organization, such as an LLC or an LLP. Assets, liabilities and ownership equity are listed as of a specific date, such as the end of its financial year. A balance sheet is often described as a "snapshot of a company's financial condition".[1] Of the four basic financial statements, the balance sheet is the only statement which applies to a single point in time of a business' calendar year.
A standard company balance sheet has three parts: assets, liabilities and ownership equity. The main categories of assets are usually listed first, and typically in order of liquidity.[2] Assets are followed by the liabilities. The difference between the assets and the liabilities is known as equity or the net assets or the net worth or capital of the company and according to the accounting equation, net worth must equal assets minus liabilities.[3]
Another way to look at the same equation is that assets equals liabilities plus owner's equity. Looking at the equation in this way shows how assets were financed: either by borrowing money (liability) or by using the owner's money (owner's equity). Balance sheets are usually presented with assets in one section and liabilities and net worth in the other section with the two sections "balancing". http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Indian mathematics emerged in the Indian subcontinent[1] from 1200 BCE[2] until the end of the 18th century. In the classical period of Indian mathematics (400 CE to 1600 CE), important contributions were made by scholars like Aryabhata, Brahmagupta, Mahāvīra, Bhaskara II, Madhava of Sangamagrama and Nilakantha Somayaji. The decimal number system in use today[3] was first recorded in Indian mathematics.[4] Indian mathematicians made early contributions to the study of the concept of zero as a number,[5] negative numbers,[6] arithmetic, and algebra.[7] In addition, trigonometry[8] was further advanced in India, and, in particular, the modern definitions of sine and cosine were developed there.[9] These mathematical concepts were transmitted to the Middle East, China, and Europe[7] and led to further developments that now form the foundations of many areas of mathematics.
Ancient and medieval Indian mathematical works, all composed in Sanskrit, usually consisted of a section of sutras in which a set of rules or problems were stated with great economy in verse in order to aid memorization by a student. This was followed by a second section consisting of a prose commentary (sometimes multiple commentaries by different scholars) that explained the problem in more detail and provided justification for the solution. In the prose section, the form (and therefore its memorization) was not considered so important as the ideas involved. All mathematical works were orally transmitted until approximately 500 BCE; thereafter, they were transmitted both orally and in manuscript form. The oldest extant mathematical document produced on the Indian subcontinent is the birch bark Bakhshali Manuscript. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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This is the simulation of projectile motion in excel. Angle of throw is between the direction of throw and the perpendicular to the ground. This is a numerical simulations. No formulas are used. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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A p--n junction is a boundary or interface between two types of semiconductor material, p-type and n-type, inside a single crystal of semiconductor. It is created by doping, for example by ion implantation, diffusion of dopants, or by epitaxy (growing a layer of crystal doped with one type of dopant on top of a layer of crystal doped with another type of dopant). If two separate pieces of material were used, this would introduce a grain boundary between the semiconductors that severely inhibits its utility by scattering the electrons and holes.
p--n junctions are elementary "building blocks" of most semiconductor electronic devices such as diodes, transistors, solar cells, LEDs, and integrated circuits; they are the active sites where the electronic action of the device takes place. For example, a common type of transistor, the bipolar junction transistor, consists of two p--n junctions in series, in the form n--p--n or p--n--p.
The discovery of the p--n junction is usually attributed to American physicist Russell Ohl of Bell Laboratories.
A Schottky junction is a special case of a p--n junction, where metal serves the role of the p-type semiconductor. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Check out Ebook "Mind Math" from Dr. Garg: https://www.amazon.com/MIND-MATH-Learn-Math-Fun-ebook/dp/B017QEIF18
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Fast trick to multiple number close to 10 http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Square the number with the decimal.
Add the number to the square and add 0.25 in the end.
That is all. Check out Ebook "Mind Math" from Dr. Garg
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Net Present Value and Internal Rate of Return http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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IGOR pro tutorial. How to make graphs in IGOR? How to enter data? How to make waves in IGOR? http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Math trick to fast multiply any number with 5, 25, 125, and 15.
I am getting a lot of questions about applying this trick on odd numbers. Here is my answer.
I used even numbers to make it easy to understand. Now lets see. multiply by 5------67 x 5 = 335 (half of 67 is 33.5) Again, 67 x 25 = 1675 (1/2 of of 33.5 = 16.75) 67 x 125 = 8375 (1/2 of 16.75 = 8.375) Now it is possible that you may find it very difficult but you can do good approximation like this by choosing closer even number. 5 x 66 = 330 which is close to 335. this way you can get an idea. For exact calculation 25 x 55 = 1650 and 25 x 68 = 1700 average is 1675 http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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In probability theory, the normal (or Gaussian) distribution is a very commonly occurring continuous probability distribution—a function that tells the probability of a number in some context falling between any two real numbers. For example, the distribution of income measured on a log scale is normally distributed in some contexts, as is often the distribution of grades on a test administered to many people. Normal distributions are extremely important in statistics and are often used in the natural and social sciences for real-valued random variables whose distributions are not known.
The normal distribution is immensely useful because of the central limit theorem, which states that, under mild conditions, the mean of many random variables independently drawn from the same distribution is distributed approximately normally, irrespective of the form of the original distribution: physical quantities that are expected to be the sum of many independent processes (such as measurement errors) often have a distribution very close to the normal. Moreover, many results and methods (such as propagation of uncertainty and least squares parameter fitting) can be derived analytically in explicit form when the relevant variables are normally distributed.
The Gaussian distribution is sometimes informally called the bell curve. However, many other distributions are bell-shaped (such as Cauchy's, Student's, and logistic). The terms Gaussian function and Gaussian bell curve are also ambiguous because they sometimes refer to multiples of the normal distribution that cannot be directly interpreted in terms of probabilities. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Adding numbers is series is not that difficult if you think about it carefully... http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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This was one of the request from our subscriber. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Basic properties of logarithms (tutorial) http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Random Walk or Brownian motion (Concept and Simulations in Excel) Tutorial http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Monte Carlo methods (or Monte Carlo experiments) are a broad class of computational algorithms that rely on random sampling to obtain numerical results. They are often used in physical and mathematical problems and are most suited to be applied when it is impossible to obtain a closed-form expression or infeasible to apply a deterministic algorithm. Monte Carlo methods are mainly used in three distinct problems: optimization, numerical integration and generation of samples from a probability distribution.
Monte Carlo methods are especially useful for simulating systems with many coupled degrees of freedom, such as fluids, disordered materials, strongly coupled solids, and cellular structures (see cellular Potts model). They are used to model phenomena with significant uncertainty in inputs, such as the calculation of risk in business. They are widely used in mathematics, for example to evaluate multidimensional definite integrals with complicated boundary conditions. When Monte Carlo simulations have been applied in space exploration and oil exploration, their predictions of failures, cost overruns and schedule overruns are routinely better than human intuition or alternative "soft" methods. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Price elasticity of demand (PED or Ed) is a measure used in economics to show the responsiveness, or elasticity, of the quantity demanded of a good or service to a change in its price. More precisely, it gives the percentage change in quantity demanded in response to a one percent change in price (ceteris paribus, i.e. holding constant all the other determinants of demand, such as income). It was devised by Alfred Marshall.
Price elasticities are almost always negative, although analysts tend to ignore the sign even though this can lead to ambiguity. Only goods which do not conform to the law of demand, such as Veblen and Giffen goods, have a positive PED. In general, the demand for a good is said to be inelastic (or relatively inelastic) when the PED is less than one (in absolute value): that is, changes in price have a relatively small effect on the quantity of the good demanded. The demand for a good is said to be elastic (or relatively elastic) when its PED is greater than one (in absolute value): that is, changes in price have a relatively large effect on the quantity of a good demanded.
Revenue is maximized when price is set so that the PED is exactly one. The PED of a good can also be used to predict the incidence (or "burden") of a tax on that good. Various research methods are used to determine price elasticity, including test markets, analysis of historical sales data and conjoint analysis. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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The efficient-market hypothesis posits that stock prices are a function of information and rational expectations, and that newly revealed information about a company's prospects is almost immediately reflected in the current stock price. This would imply that all publicly known information about a company, which obviously includes its price history, would already be reflected in the current price of the stock. Accordingly, changes in the stock price reflect release of new information, changes in the market generally, or random movements around the value that reflects the existing information set. Burton Malkiel, in his influential 1973 work A Random Walk Down Wall Street, claimed that stock prices could therefore not be accurately predicted by looking at price history. As a result, Malkiel argued, stock prices are best described by a statistical process called a "random walk" meaning each day's deviations from the central value are random and unpredictable. This led Malkiel to conclude that paying financial services persons to predict the market actually hurt, rather than helped, net portfolio return. A number of empirical tests support the notion that the theory applies generally, as most portfolios managed by professional stock predictors do not outperform the market average return after accounting for the managers' fees.
While the efficient-market hypothesis finds favor among financial academics, but its critics point to instances in which actual market experience differs from the prediction-of-unpredictability the hypothesis implies. A large industry has grown up around the implication proposition that some analysts can predict stocks better than others; ironically that would be impossible under the Efficient Markets Hypothesis if the stock prediction industry did not offer something its customers believed to be of value.

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"Is there an easy way to calculate ? " I am sure you must have asked this question at least once in your life. Have you ever wondered why some people are so good at number crunching, while others struggle to add even the single digits correctly or without straining their mind. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Factorial, Permutations, Combinations for DUMMIES http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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How to calculate pH of solutions http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Internal rate of return (IRR) and Net present value (NPV) in excel without using commands http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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There are two prices that are critical for any investor to know: the current price of the investment he or she owns, or plans to own, and its future selling price. Despite this, investors are constantly reviewing past pricing history and using it to influence their future investment decisions. Some investors won't buy a stock or index that has risen too sharply, because they assume that it's due for a correction, while other investors avoid a falling stock, because they fear that it will continue to deteriorate. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Despite the sophisticated composition of most volatility forecasting models, critics claim that their predictive power is similar to that of plain-vanilla measures, such as simple past volatility [9][10] especially out-of-sample, where different data are used to estimate the models and to test them.[11] Other works have agreed, but claim critics failed to correctly implement the more complicated models.[12] Some practitioners and portfolio managers seem to completely ignore or dismiss volatility forecasting models. For example, Nassim Taleb famously titled one of his Journal of Portfolio Management papers "We Don't Quite Know What We are Talking About When We Talk About Volatility".[13] In a similar note, Emanuel Derman expressed his disillusion with the enormous supply of empirical models unsupported by theory.[14] He argues that, while "theories are attempts to uncover the hidden principles underpinning the world around us, as Albert Einstein did with his theory of relativity", we should remember that "models are metaphors -- analogies that describe one thing relative to another". http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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After applying an arithmetic operation to two operands and getting a result, you can use this procedure to improve your confidence that the result is correct.
Sum the digits of the first operand; any 9s (or sets of digits that add to 9) can be counted as 0.
If the resulting sum has two or more digits, sum those digits as in step one; repeat this step until the resulting sum has only one digit.
Repeat steps one and two with the second operand. You now have two one-digit numbers, one condensed from the first operand and the other condensed from the second operand. (These one-digit numbers are also the remainders you would end up with if you divided the original operands by 9; mathematically speaking, they're the original operands modulo 9.)
Apply the originally specified operation to the two condensed operands, and then apply the summing-of-digits procedure to the result of the operation.
Sum the digits of the result you originally obtained for the original calculation..
If the result of step 4 does not equal the result of step 5, then the original answer is wrong. If the two results match, then the original answer may be right, though it isn't guaranteed to be. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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Two events are 'mutually exclusive' if they cannot occur at the same time. An example is tossing a coin once, which can result in either heads or tails, but not both.
In the coin-tossing example, both outcomes are collectively exhaustive, which means that at least one of the outcomes must happen, so these two possibilities together exhaust all the possibilities. However, not all mutually exclusive events are collectively exhaustive. For example, the outcomes 1 and 4 of a single roll of a six-sided die are mutually exclusive (cannot both happen) but not collectively exhaustive (there are other possible outcomes; 2,3,5,6). http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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In finance, an option is a contract which gives the owner the right, but not the obligation, to buy or sell an underlying asset or instrument at a specified strike price on or before a specified date. The seller incurs a corresponding obligation to fulfill the transaction, that is to sell or buy, if the long holder elects to "exercise" the option prior to expiration. The buyer pays a premium to the seller for this right. An option which conveys the right to buy something at a specific price is called a call; an option which conveys the right to sell something at a specific price is called a put. Both are commonly traded, though in basic finance for clarity the call option is more frequently discussed, as it moves in the same direction as the underlying asset, rather than opposite, as does the put. http://www.garguniversity.com Check out Ebook "Mind Math" from Dr. Garg
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