is high The formulas for standard deviation are given below but you should look at the examples first Population mean Population variance method 1 ‚ Population variance method 2 ‚ (it does not matter what method you use both give the same answer‚ the only thing you need to know about variance is that it is population standard deviation squared so if variance is high then standard deviation is high Population standard deviation σ = Example 1 find the population mean μ and population standard
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included in the model are publicly traded financial assets such as bonds and stocks. Investors borrow or lend at a risk free rate. Investors have no transactions cost and do not pay taxes on returns • All investors in the market are rational mean variance optimisers. • Finally‚ investors have homogenous expectations which imply that they analyse securities in the same way‚ share the same economic view of the world‚ therefore they share identical estimates of probability distributions of cash
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Chapter 1 1(4). The risk premium is defined as the rate of return on A. A risky asset minus the inflation rate B. The overall market C. A Treasury bill D. A risky asset minus the risk-free rate E. A risk-less investment Answer: D 2(5). The variance measure the: Non-graded A. Total difference between the actual returns and the average returns B. Average difference between the actual squared returns and the risk-free returns C. Average squared difference between the actual returns
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(where the simple model is nested within the complicated one). One case where the distribution of the test statistic is an exact chi-squared distribution is the test that the variance of a normally distributed population has a given value based on a sample variance. Such a test is uncommon in practice because values of variances to test against are seldom known
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1. A quality control engineer knows that 10% of the microprocessor chips produced by a machine are defective. Out of a large shipment‚ five chips are chosen at random. What is the probability that none of them is defective? What is the probability that at least one is defective? 2. An automated manufacturing process produces a component with an average width of 7.55 centimeters‚ with a standard deviation of 0.02 centimeter. All components deviating by more than 0.05 centimeter from the mean must
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than 10 minutes for a bus. 3. A recent study indicates that the annual cost of maintaining and repairing a car in a town in Ontario averages 200 with a variance of 260. If a tax of 20% is introduced on all items associated with the maintenance and repair of cars (i.e.‚ everything is made 20% more expensive)‚ what will be the variance of the annual cost of maintaining and repairing a car? (Ans: 374) 4. The time to failure of a component in an electronic device has an exponential distribution
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0.0749 + 0.0749 = 0.1498. 2. [§8-53] Let X1 ‚ . . . ‚ Xn be i.i.d. uniform on [0‚ θ]. (a) Find the method of moments estimate of θ‚ and the mean‚ variance‚ bias‚ and MSE of the MME. (b) The mle of θ is θˆ = max Xi . The pdf of max1≤i≤n Xi (How do we 1≤i≤n find this? ) is n−1 nx f (x|θ) = θn 0 0<x<θ . otherwise Calculate the mean and variance of the mle.
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Using EXCEL for Asset Allocation and Performing Market Efficiency Studies 1. Introduction There are several features in EXCEL that are very useful for asset allocation and performing market efficiency studies. These features used in conjunction with live or historical data allows one to apply the sophisticated techniques discussed in this class in practical situations. This write-up will introduce students to the various mathematical and statistical functions available in EXCEL and explain
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learning various statistical techniques and their applications that will assist you in making business decisions. • Enable students to perform and understand statistical analysis of data‚ with the view of being able to critically evaluate statistical reports or findings • Learn to think critically about how statistics is used by others and how it impacts your day to day life and career No mathematical background beyond high school algebra is required for an understanding of the material 3 Course Requirements
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| Basic math symbols Symbol | Symbol Name | Meaning / definition | Example | = | equals sign | equality | 5 = 2+3 | ≠ | not equal sign | inequality | 5 ≠ 4 | > | strict inequality | greater than | 5 > 4 | < | strict inequality | less than | 4 < 5 | ≥ | inequality | greater than or equal to | 5 ≥ 4 | ≤ | inequality | less than or equal to | 4 ≤ 5 | ( ) | parentheses | calculate expression inside first | 2 × (3+5) = 16 | [ ] | brackets | calculate expression inside first
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