Question

Compute the distribution of X+Y in the following cases:X and Y are independent Poisson random variables with means respective \lambda_{1} and \lambda_{2}.

Random variables
ANSWERED
asked 2021-06-03

Compute the distribution of \(X+Y\) in the following cases:
X and Y are independent Poisson random variables with means respective \(\lambda_{1} and \lambda_{2}\).

Expert Answers (1)

2021-06-04

\(X\sim P(\lambda_{1})\)
\(X\sim P(\lambda_{2})\)
X and Y are independent
\(P(\lambda_{1})+P(\lambda_{2})\sim P(\lambda_{1}+\lambda_{2})\)
So,
\(X+Y\) follows poisson distribution.
\((X+Y)\sim P(\lambda_{1}+\lambda_{2})\)

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