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So take this example.

The number of ice creams sold per hour from Mr Fishy’s van is observed to be a Poisson random variable with parameter λ = 8. Each ice cream costs two pounds but Mr Fishy has to pay five pounds per hour for the pitch. What is the variance of his hourly profit?

Now I think this is a perfect example to illustrate how badly I understand the poisson distribution. I took λ = 8 and multiplied it by 2. Then took away £5 to get £11. It was wrong.

Can someone please explain where I went wrong?

Tingo Hugo
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    By the rules of the variance you have to square coefficients and drop additive constants. Try to formally define the hourly profit as a random variable, and then compute the variance using its basic properties and the variance of the Poisson distribution. – Matija Jan 15 '23 at 22:38
  • So, Var(2Y-5) = 4Var(Y) = 32. Gotcha thx – Tingo Hugo Jan 15 '23 at 22:42

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