How to do the linear transformation of a random variable

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CORRECT

CORRECT

Variable has a Poisson distribution with a mean of . What is the variance of Variable ?

$\sigma^{2} = 25$

CORRECT

$\sigma^{2} = 20$

$\sigma^{2} = 400$

$\sigma^{2} = 105$

$\sigma^{2} = 130$

Because has a Poisson distribution we know that:

$E(A)=\mu$ and

$V(A)=\sigma^2=\mu$ .

Therefore, since we are given the mean of 25, we can find its variance to also be 25.