How to find variance for given problem?

Question

Suppose the expected earnings for a farm depends on the number of worms per apple. The number of worms per apple has a Poisson distribution with mean 0.32.

a) The expected earnings per apple depends on number of defects: 13-5X. What is the expected earning for 10 apples? answer: I have done this part, where I do 10 * (13-5*0.32) which is the right answer.

b) Find the variance of earnings for 10 apples.

This is where I'm stuck. Thanks for any help

Answer 1

Hints:

• If $X$ has variance $\sigma^2$ and $Y=aX+b$ then $Y$ has variance $a^2 \sigma^2$
• The variance of the sum of independent random variables is equal to the sum of their variances
• The variance of a Poisson distribution is equal to its mean