Let Y1, Y2, . . . , Yn be independent Poisson random

QUESTION:

Let \(Y_{1}, Y_{2}, \ldots, Y_{n}\) be independent Poisson random variables with means \(\lambda_{1}, \lambda_{2} \ldots \ldots \lambda_{n}\). respectively. Find the

a probability function of \(\sum_{i=1}^{n} Y_{i}\).

b conditional probability function of \(Y_1\), given that \(\sum_{i=1}^{n} Y_{i}=m\).

c conditional probability function of \(Y_{1}+Y_{2}\), given that \(\sum_{i=1}^{n} Y_{i}=m\).

Equation Transcription:

Text Transcription:

Y_1,Y_2,...,Y_n

lamda_1,lamda_2......lamda_n

sum_i=1^n Y_i

 Y1

sum_i=1^n Y_i=m

Y_1+Y_2