Answer:
Step-by-step explanation:
Let X be the number of snowstorms
let Y be the paid amount
Call one unit of money 10,000
If X = 0 or 1 then y = 0
X = 2 then y = 1 so on ...
E(Y) = [tex]\sum_{k=2}^{\infty}(k-1)P[X=k][/tex]
= [tex]\sum_{k=2}^{\infty}(k-1)e^{^{-1.5}}\frac{(1.5)^{k}}{k!}[/tex]
= [tex]\sum_{k=1}^{\infty}(k-1)e^{^{-1.5}}\frac{(1.5)^{k}}{k!}[/tex]
= [tex]\sum_{k=1}^{\infty}ke^{^{-1.5}}\frac{(1.5)^{k}}{k!}[/tex] - [tex]\sum_{k=1}^{\infty}e^{^{-1.5}}\frac{(1.5)^{k}}{k!}[/tex]
= [tex]\sum_{k=0}^{\infty}ke^{^{-1.5}}\frac{(1.5)^{k}}{k!}[/tex]-(-[tex]e^{-1.5}[/tex] +[tex]\sum_{k=0}^{\infty}e^{^{-1.5}}\frac{(1.5)^{k}}{k!}[/tex] )
= 1.5 +[tex]e^{-1.5}[/tex] - 1 ≈ 0.7231
