Connie tosses a fair coin three times If X X1 X2 where X1

Connie tosses a fair coin three times. If X = X1 - X2, where X1 counts the number of

heads that result and X2 counts the number of tails that result, determine the probability

distributions for X1, X2, and X

Solution

Outcomes : {HHH , HHT , HTH , HTT , THH , THT , TTH , TTT }

X1 = 12

X2 = 12

X = 12-12 = 0

Therefore,

P(X1) = 12/24 = 1/2

P(X2) = 12/24 = 1/2

P(X)   = 0