Chapter 2: Problem 2
Let \(f_{1 \mid 2}\left(x_{1} \mid x_{2}\right)=c_{1} x_{1} / x_{2}^{2},
0
Chapter 2: Problem 2
Let \(f_{1 \mid 2}\left(x_{1} \mid x_{2}\right)=c_{1} x_{1} / x_{2}^{2},
0
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Get started for freeIf \(X\) has the pdf of \(f(x)=\frac{1}{4},-1
Let \(f\left(x_{1}, x_{2}\right)=4 x_{1} x_{2}, 0
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 \(A_{1}=\\{(x, y): x \leq 2, y \leq 4\\}, A_{2}=\\{(x, y): x \leq 2, y \leq
1\\}, A_{3}=\)
\(\\{(x, y): x \leq 0, y \leq 4\\}\), and \(A_{4}=\\{(x, y): x \leq 0 y \leq
1\\}\) be subsets of the
space \(\mathcal{A}\) of two random variables \(X\) and \(Y\), which is the entire
two-dimensional plane. If \(P\left(A_{1}\right)=\frac{7}{8},
P\left(A_{2}\right)=\frac{4}{8}, P\left(A_{3}\right)=\frac{3}{8}\), and
\(P\left(A_{4}\right)=\frac{2}{8}\), find \(P\left(A_{5}\right)\), where
\(A_{5}=\\{(x, y): 0
. If \(f(x)=\frac{1}{2},-1
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