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(a) Let X and Y be two independent random variables. Suppose that we know Var (2X- Y) 6 and Var(X+2Y) = 9. Find Var(X) and Var(Y). (b) Let X1 and X2 be independent exponential random variables with rates μ₁ and 2. Find the conditional density of X₁ given that X₁+X2=t.

(a) Let X and Y be two independent random variables. Suppose that we know Var (2X- Y) 6 and Var(X+2Y) = 9. Find Var(X) and Var(Y). (b) Let X1 and X2 be independent exponential random variables with rates μ₁ and 2. Find the conditional density of X₁ given that X₁+X2=t.

MATLAB: An Introduction with Applications
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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(a) Let X and Y be two independent random variables. Suppose that we know Var (2X- Y) 6 and Var(X+2Y) = 9. Find Var(X) and Var(Y). (b) Let X1 and X2 be independent exponential random variables with rates μ₁ and 2. Find the conditional density of X₁ given that X₁+X2=t.
Transcribed Image Text:(a) Let X and Y be two independent random variables. Suppose that we know Var (2X- Y) 6 and Var(X+2Y) = 9. Find Var(X) and Var(Y). (b) Let X1 and X2 be independent exponential random variables with rates μ₁ and 2. Find the conditional density of X₁ given that X₁+X2=t.
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