1 answer

(b) A company prices its hurricane insurance usng the following assumptsons (i) In any calendar year,...

Question:

(b) A company prices its hurricane insurance usng the following assumptsons (i) In any calendar year, there can be at most on

ii. (6 points) calculate the probability that there are fewer than 3 hurricanes. /-X

(b) A company prices its hurricane insurance usng the following assumptsons (i) In any calendar year, there can be at most one hurricane (1) In any calendar year, the probability of a hurricane is 0.05 (iii) The mumber of hurricanes in any calendar year is independent of the number of hurricanes in any other calendar year e .os Using the company's assumptions, for a 20-year period i (10 points) what are the expected value and standard deviation of the number of hurricanes?
ii. (6 points) calculate the probability that there are fewer than 3 hurricanes. /-X

Answers

i) Define Xi=number of hurricanes in i th  year, i=1,2,..,20

Then Xi is either 0 or 1.

The probability p of a hurricane is .05

Y=X1+...+X20 is the total number of hurricanes in 20 years.

E(Y)=EX1+...+EX20=20*.05=1 (as E(Xi)=.05)

Var(Y)=Var(X1)+...+Var(X20) due to independence.

Var(Xi)=E(Xi2)-E2(Xi)=.05-.05*.05=.0475

Var(Y)=20*.0475= 0.95
SD(Y)=square root of Var(Y)= 0.9746794

ii) P(There are fewer than 3 hurricanes)=P(Y<3)=P(Y<=2)= 0.9245163

For query, comment.

.

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