Question-39

Poisson Distribution

If \(X\) and \(Y\) are independent Poisson variates such that

\(P(X = 1) = P(X=2)\) and \(P(Y = 2) = P(Y=3)\). Find the variance of \(X-2Y\).

Hint

Define \(X \sim P(\lambda_1)\) and \(Y \sim P(\lambda_2)\). Use PMF formula of Poisson distribution for the given equation and find the values of \(\lambda_1\) and \(\lambda_2\). Then, find the required value, \(V(X-2Y)\), by using the values of \(\lambda_1\) and \(\lambda_2\) as \(V(X) = \lambda_1\) and \(V(Y) = \lambda_2\).

Answer

Solution