Statistics for the Behavioral Sciences
Statistics for the Behavioral Sciences
2nd Edition
ISBN: 9781452286907
Author: Gregory J. Privitera
Publisher: SAGE Publications, Inc
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Chapter 13, Problem 12FP
To determine

Observe the change in the power of the within-subjects design if the consistency of changes in the dependent variable across the groups increases.

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A random variable X takes values 0 and 1 with probabilities q and p, respectively, with q+p=1. find the moment generating function of X and show that all the moments about the origin equal p. (Note- Please include as much detailed solution/steps in the solution to understand, Thank you!)
1 (Expected Shortfall) Suppose the price of an asset Pt follows a normal random walk, i.e., Pt = Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²). Po+r1+. ⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price in T days, i.e., VaRq(Pt – Pt–T). - • If ESq(rt) = A, find ES₁(Pt – Pt–T).
2 (Normal Distribution) Let rt be a log return. Suppose that r₁, 2, ... are IID N(0.06, 0.47). What is the distribution of rt (4) = rt + rt-1 + rt-2 + rt-3? What is P(rt (4) < 2)? What is the covariance between r2(2) = 1 + 12 and 13(2) = r² + 13? • What is the conditional distribution of r₁(3) = rt + rt-1 + rt-2 given rt-2 = 0.6?
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