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
All the tools & learning materials you need for study success - in one app.
Get started for freeLet 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?
Let \(X_{1}, X_{2}\) be two random variables with joint pdf \(f\left(x_{1},
x_{2}\right)=x_{1} \exp \left\\{-x_{2}\right\\}\), for \(0
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
Let the random variables \(X_{1}\) and \(X_{2}\) have the joint pmf described as follows: $$\begin{array}{c|cccccc}\left(x_{1}, x_{2}\right) & (0,0) & (0,1) & (0,2) & (1,0) & (1,1) & (1,2) \\ \hline f\left(x_{1}, x_{2}\right) & \frac{2}{12} & \frac{3}{12} & \frac{2}{12} & \frac{2}{12} & \frac{2}{12} & \frac{1}{12} \end{array}$$ and \(f\left(x_{1}, x_{2}\right)\) is equal to zero elsewhere. (a) Write these probabilities in a rectangular array as in Example 2.1.3, recording each marginal pdf in the "margins". (b) What is \(P\left(X_{1}+X_{2}=1\right) ?\)
Let \(f\left(x_{1}, x_{2}\right)=21 x_{1}^{2} x_{2}^{3}, 0
What do you think about this solution?
We value your feedback to improve our textbook solutions.