4. [4] Suppose you buy a ticket from each of the Arkansas and Missouri loteries.

Question

4. [4] Suppose you buy a ticket from each of the Arkansas and Missouri loteries. The Arkansas lottery has an expected value of-1 (dollars) with a standard deviation of S0.25. The Missouri lottery has an expected value of 2 (dollars) with a standard deviation of $0.35. a. What is the expected value of the total winnings for playing both games? b. What is the standard deviation of the total winnings for playing both games? 5. 12] Which, if any, of the following is/are not required for a binomial probability distribution? a) Each trial is independent of the others b) Each trial must have two outcomes, "success"or "failure". c) There is a fixed number,n, of trials. d) The probability, p, of a success must be the same from trial to trial e) The mean of the distribution is np

Explanation / Answer

let X and Y are outcome of Arkansas and Missouri lotteries

a)

expected value of total winning E(X+Y) =E(X)+E(Y) =-1-2 =-3

b)

std deviation of total winning =(Var(X)+Var(Y))1/2 =(0.252+0.352)1/2 =0.43

5)

all are true for binomial disirbution;

(however option e is the outcome and not the requirement of binomial distirbution)

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