7. Suppose you are sponsoring a fundraising dinner for your favorite political c

Question

7. Suppose you are sponsoring a fundraising dinner for your favorite political candidate. You are not sure how many people wll attend. Based on past dinners, the probability distribution for the attendance (or #people who attend), denoted as X, looks like this: Attendance (X) foo 0.1 0.2 100 200 300 400 00 0.2 0.3 0.2 (1) (3 points) First calculate the expected attendance E(X) (2) 6 points) Suppose you make a profit of S40 for each person attending. Calculate the expected value and the standard deviation of your total profit

Explanation / Answer

a) E[X] = X*P(X) = 100*0.1 + 200*0.2 + 300*0.3 + 400*0.2 + 500*0.2 = 320

b)

E[X] = X*P(X) = 4000*0.1 + 8000*0.2 + 12000*0.3 + 16000*0.2 + 20000*0.2 = 12800

`V(X) = (X-E[X])2*P(X) = (4000-12800)2*0.1 + (8000-12800)2*0.2 + (12000-12800)2*0.3 + (16000-12800)2*0.2 + (20000-12800)2*0.2 = 24960000

std. dev = sqrt(24960000) = 4996.00

X 4000 8000 12000 16000 20000 P(X) 0.1 0.2 0.3 0.2 0.2

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