Refer to Exercises 5.7, 5.25, and 5.51. Let Y1 and Y2 have

QUESTION:

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 \(V\left(Y_{1}-Y_{2}\right)\)?

Equation Transcription:

Text Transcription:

Y_1

Y_2

f(y_1,y_2)={_0,     elsewhere. ^e^-(y_1+y_2),     y_1>0,y_2>0

E(Y_1+Y_2)

V(Y_1+Y_2)

P(Y_1-Y_2>3)

P(Y_1-Y_2<-3)

E(Y_1-Y_2)

V(Y_1-Y_2)

V(Y_1+Y_2)

V(Y_1-Y_2)