All voters of Milwaukee County were asked a week before election day whether the
ID: 3305747 • Letter: A
Question
All voters of Milwaukee County were asked a week before election day whether they would vote for a certain presidential candidate. Of these, 48% answered yes, 45% replied no, and the rest were undecided. If a yes answer is coded +1, a no is coded -1, and undecided us coded 0, find the mean and variance of the code.
As a marketing researcher of a toy manufacturing firm, you must decide on which of two new games to întroduce this year. The probability distríbutions for their net annual profits (in Smillions) are listed in the following table. Game A Game B Net Profit Subjective Prob 0.1 0.2 0.4 0.3 Net Profit 0 Subjective Prob 0.2 0.3 0.3 0.2 Demonstrate that each is a probability distribution. b.What is the probability that Game A will be profitable? Game B? Calculate the expected value for both Game A and B Calculate the standard deviation for both Game A and Game B hich game should they produce and why?Explanation / Answer
A) To be a valid probability distribution, the total sum of all probability must be equal to 1.
Total probability for game A = 0.1 + 0.2 + 0.4 + 0.3 = 1
Total probability for game B = 0.2 + 0.3 + 0.3 + 0.2 = 1
So, both of them are probability distribution
B) P(game A will be profitable) = P(3) + P(6) = 0.4 + 0.3 = 0.7
P(game B will be profitable) = P(1) + P(3) + P(5) = 0.3 + 0.3 + 0.2 = 0.8
C) E(X game A) = - 5*0.1 + 0*0.2 + 3*0.4 + 6*0.3 = 2.5
E(X game B) = 0*0.2 + 1*0.3 + 3*0.3 + 5*0.2 = 2.2
D) E(X2 game A) = (-5)2*0.1 + 02*0.2 + 32*0.4 + 62*0.3 = 16.9
Var(X game A) = E(X2) - (E(X))2 = 16.9 - 2.52 = 10.65
Standard deviation of game A = sqrt(10.56) = 3.25
E(X2 game B) = 02*0.2 + 12*0.3 + 32*0.3 + 52*0.2 = 8
Var (X game B) = E(X2) - (E(X))2 = 8 - 2.22 = 3.16
Standard deviation of game B = sqrt(3.16) = 1.78
E) first game should be played as expected value is high