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Let X follows Poisson distribution with parameter $\lambda\gt0$ and $Y=aX$, where $a\gt0$ is a constant.

Q. What will be the $PMF$ of $Y$?

Since by using the M.G.F we have $M_Y(t)=M_X(at)=(e^{\lambda(e^{at}-1)})$. What next I should do to derive its distribution.

mandez
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user2586518
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  • $Y$ takes the values $ak$ where $k$ is a non-negative integer with probability $e^{-\lambda}\lambda ^k/k!$. – Patissot May 09 '15 at 10:50
  • Hello, welcome to Math Stack Exchange! To use $\LaTeX$, you should put the formula between dollar signs. – wythagoras May 09 '15 at 10:54

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