(1) Let X and Y be independent random variables with distributions 1 y 1 Pr(X = r) Pr(Y = y) 1 Let Z = XY. (i) Find E(Y). (ii) Find Var(Y). (iii) Write down a table giving the probability distribution...

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(1) Let X and Y be independent random variables with distributions<br>1<br>y<br>1<br>Pr(X = r)<br>Pr(Y = y)<br>1<br>Let Z = XY.<br>(i) Find E(Y).<br>(ii) Find Var(Y).<br>(iii) Write down a table giving the probability distribution for Z.<br>(iv) Are the random variables X and Z independent?<br>

Extracted text: (1) Let X and Y be independent random variables with distributions 1 y 1 Pr(X = r) Pr(Y = y) 1 Let Z = XY. (i) Find E(Y). (ii) Find Var(Y). (iii) Write down a table giving the probability distribution for Z. (iv) Are the random variables X and Z independent?

Jun 03, 2022

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(1) Let X and Y be independent random variables with distributions 1 y 1 Pr(X = r) Pr(Y = y) 1 Let Z = XY. (i) Find E(Y). (ii) Find Var(Y). (iii) Write down a table giving the probability distribution...

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