Chapter 2: Problem 6
Let \(X\) and \(Y\) have the joint pdf \(f(x, y)=1,-x
Chapter 2: Problem 6
Let \(X\) and \(Y\) have the joint pdf \(f(x, y)=1,-x
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Get started for freeLet \(X_{1}, X_{2}, X_{3}\) be iid with common pdf \(f(x)=e^{-x}, x>0,0\) elsewhere. Find the joint pdf of \(Y_{1}=X_{1}, Y_{2}=X_{1}+X_{2}\), and \(Y_{3}=X_{1}+X_{2}+X_{3}\)
Suppose \(X_{1}\) and \(X_{2}\) are random variables of the discrete type which have the joint pmf \(p\left(x_{1}, x_{2}\right)=\left(x_{1}+2 x_{2}\right) / 18,\left(x_{1}, x_{2}\right)=(1,1),(1,2),(2,1),(2,2)\), zero elsewhere. Determine the conditional mean and variance of \(X_{2}\), given \(X_{1}=x_{1}\), for \(x_{1}=1\) or 2. Also compute \(E\left(3 X_{1}-2 X_{2}\right)\).
Let \(f\left(x_{1}, x_{2}\right)=21 x_{1}^{2} x_{2}^{3}, 0
Let \(X_{1}\) and \(X_{2}\) have the joint pdf \(f\left(x_{1},
x_{2}\right)=x_{1}+x_{2}, 0
Let the random variables \(X_{1}\) and \(X_{2}\) have the joint pdf \(f\left(x_{1}, x_{2}\right)=1 / \pi\), for \(\left(x_{1}-1\right)^{2}+\left(x_{2}+2\right)^{2}<1\), zero elsewhere. Find \(f_{1}\left(x_{1}\right)\) and \(f_{2}\left(x_{2}\right) .\) Are \(X_{1}\) and \(X_{2}\) independent?
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