Question

The number of heavy snowfalls at a ski resort has the following distribution:

Number of heavy snowfalls 0 1 2 3 4 5 or more

Probability 0.10 0.25 0.30 0.20 0.10 0.05

An insurance policy pays a benefit of:

5, 000(X − 5)^2

where X is the number of heavy snowfalls in a given year, up to a maximum of 5. Calculate the expected benefit under this policy.

A. 37,500

B. 42,500

C. 45,000

D. 49,500

E. 50,500

Answer 1

X : number of heavy snowfalls in a given year

An insurance policy pays a benefit of 5000(X-5) ²

x	p	y=5000(X-5)2	p*y
0	0.1	125000	12500
1	0.25	80000	20000
2	0.3	45000	13500
3	0.2	20000	4000
4	0.1	5000	500
5	0.05	0	0
Total			50500

Now,

the expected benefit under this policy =

= 50500

So, the correct option is E. 50,500