Solved: Refer to Exercises 5.6, 5.24, and 5.50. Suppose that a radioactive particle is
Chapter 5, Problem 5.75(choose chapter or problem)
Refer to Exercises 5.7, 5.25, and 5.51. Let \(Y_{1}\) and \(Y_{2}\) have joint density function
\(f\left(y_{1}, y_{2}\right)=\left\{\begin{array}{ll}
e^{-\left(y_{1}+y_{2}\right)}, & y_{1}>0, y_{2}>0 \\
0, & \text { elsewhere. }
\end{array}\right.\)
a What are \(E\left(Y_{1}+Y_{2}\right)\) and \(V\left(Y_{1}+Y_{2}\right)\)?
b What is \(P\left(Y_{1}-Y_{2}>3\right)\)?
c What is \(P\left(Y_{1}-Y_{2}<-3\right)\)?
d What are \(E\left(Y_{1}-Y_{2}\right)\) and \(V\left(Y_{1}-Y_{2}\right)\)?
e What do you notice about \(V\left(Y_{1}+Y_{2}\right)\) and \(V\left(Y_{1}-Y_{2}\right)\)?
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