In a hotly contested presidential election, suppose the outcome is to be determined by the results in 4 battleground states: Arizona, Georgia, Pennsylvania, and Wisconsin, with 11,16, 20, and 10 electoral votes, respectively. One of the candidates, Mr. B, has already gathered 249 electoral votes elsewhere. He needs an additional 21 electoral votes from these 4 battleground states to win the election. Mr. B is equally likely to win or lose each of these 4 battle ground states, and the outcomes in different battleground states are independent. Let N denote the number of states among these 4 that Mr. B will win.
Let M denote the number of electoral votes Mr. B will win from these 4 battleground states. Compute the mean and variance of M.
I know there are 16 possible total votes Mr. B can get (0, 10, 11, 16, 20, ...). Is each total equally likely? I got my mean, E(M) = 456/16 = 28.5 but I'm not sure if this is the right approach.
Yes, given that Mr. B is equally likely to win or lose and since the outcomes are independent, it does translate to all 16 possibilities being equally likely.