Question

Suppose you buy a raffle ticket in each of 25 consecutive weeks in support of your favorite charity. one of the 1200 raffle tickets sold each week pays $2000. what do you expect to win for those 25 weeks, and with what standard deviation?

Answer 1

a. Let x be the cost of 1 raffle ticket
then -x (1199/1200) + (2000-x) (1/1200) = 0
-1199x/1200 + 2000 / 1200 - x/1200 = 0 -1200x / 1200 =- 2000/1200 x= $1.67
So your expected value per game is
-1.67(1199/1200)+1998.33(1/1200)=0

b. Since your random variable takes on only 2 values,
which is just the square of the standard deviation
(1998.33-1.67)^2(1/1200)(1199/1200) = 3319.44
Therefore, the answer is win about $0, give or take about $58.