15. Let Y1, Y2, and Y3 be independent, N(0, 1)-distributed random variables,and setX1 = Y1 - Y3,X2 = 2Y1 + Y- 2Y3,X3 = -2Y1 +3Y3.Determine the conditional distribution of X2 given that X1 +X3 r.

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Answered: Let Y1, Y2, and Y3 be independent, N(0,…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Consider a financial asset (for instance a stock) and assume its value today is $100. Let X; be the change in value of the asset (in $) on day i. After 60 days, the value of the asset will be X = 100+ X₁+X2+...+X60- We model these unknown price changes, X,, as random variables with the properties: The random variables X, are independent. ⚫ The random variables X, have expected value $0.3 and standard deviation $1.2. (a) Estimate the probability that we make a gain in our investment, i.e. P(X >$100). You may use the table in the appendix.
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Exercise 12. Let X, Y, Z ~ N(0, 1) be independent. Determine the distribution, expectation and variance of the following random variables: a) X + Y + Z b) X² + y² + Z²

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Let Y1, Y2, and Y3 be independent, N(0, 1)-distributed random variables, and set X1 = Y1 - Y3, X2 2Y + Y2 - 2Y3, X3 =-2Y1 + 3Y3. %3D Determine the conditional distribution of X2 given that XT+ X3z.