Let Y1 and Y2 be independent random variables, each having

Chapter 6, Problem 104SE

(choose chapter or problem)

Let \(\mathrm{Y}_{1} \text { and } \mathrm{Y}_{2}\) be independent random variables, each having the same geometric distribution.

Find \(P\left(Y_{1}=Y_{2}\right)=P\left(Y_{1}-Y_{2}=0\right)\). [Hint: Your answer will involve evaluating an infinite geometric series. The results in Appendix A1.11 will be useful.]Find \(P\left(Y_{1}-Y_{2}=1\right)\).If \(U=Y_{1}-Y_{2}\), find the (discrete) probability function for U. [Hint: Part (a) gives

\(\mathrm{P}(\mathrm{U}=0)\), and part (b) gives \(\mathrm{P}(\mathrm{U}=1)\). Consider the positive and negative integer values for U separately.]

Equation Transcription:

Text Transcription:

Y1 and Y2

P(Y1 = Y2)=P(Y1 - Y2=0)

P(Y1 - Y2=1)

U=Y1 - Y2

P(U= 0)

P(U= 1)