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