Only the answer to Question D and E please 3. Three areas of southern California

Question

Only the answer to Question D and E please

3. Three areas of southern California are prime candidates for forest fires each dry season. You believe (based on historical evidence) that each of these areas, independently of the others, has a 30% chance of having a major forest fire in the next dry season. a. Find the probability distribution of X, the number of the three regions that have major forest fires in the next dry season. b. What is the probability that none of the areas will have a major forest fire? c. What is the probability that all of them will have a major forest fire? d. What are the expected value, variance, and standard deviation for the number of regions with major forest fires? e. Each major forest fire is expected to cause $20 million in damage and other expenses. What are the expected value, variance, and standard deviation for the amount of damage and other expenses in these three regions in the next dry season?

Explanation / Answer

d) expected value E(X)=np=3*0.3 =0.9

Variance V(X)=np(1-p)=0.63

standard deviation SD(X)=(0.63)1/2 =0.7937

e) jhere as expense Y =20X

hence mean E(Y)=20*E(X)=20*0.9 =18 million

Variance of Y =V(Y)=202*Var(X) =252

std deviaiton of Y SD(Y)=20*SD(X) =15.8745 million

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