Refer to Exercise 6.52. Suppose that W = Y1 + Y2 where Y1

QUESTION:

Refer to Exercise 6.52. Suppose that \(W=Y_{1}+Y_{2}\) where \(Y_{1} \text { and } Y_{2}\) are independent. If  \(W\) has a Poisson distribution with mean \(\lambda \text { and } W_{1}\) has a Poisson distribution with mean \(\lambda_{1}<\lambda\)  show that \(Y_{2}\) has a Poisson distribution with mean \(\lambda-\lambda_{1}\)

Equation Transcription:

Text Transcription:

W=Y_1+Y_2

Y_1 and Y_2

W

\lambda and W_1

\lambda_1<\lambda

Y_2

\lambda-\lambda_1