Chapter 2 Section 3 Question 12
Question
Let $X$ ~ $Poisson(\lambda)$. Let $Y = X - 7$. What is the probability function of Y?
Answer
Author: Mohammad-Ali Bandzar| Date:Oct 16 2020
From Example 2.3.6 in the book we know: $$p\scriptsize{Y}\normalsize{(y)=P(Y=y)=\frac{\lambda^y}{y!}e^{-\lambda}}$$
We know that we want the probability of X for $y+7$ therefore: $$p_{Y}(y))=P(X=y+7)$$ $$p_{Y}(y))=\frac{\lambda^{y+7}}{(y+7)!}*e^{-\lambda}$$