involving the flipping of a loaded coin, but assume that Pr[H]=0.3 Also, assume that the coin is flipped 3 times, and the random variable XX is defined to be 4 times

Question

 involving the flipping of a loaded coin, but assume that Pr[H]=0.3Pr[H]=0.3. Also, assume that the coin is flipped 3 times, and the random variable XX is defined to be 4 times the number of heads minus 2 times the number of tails.

Fill in the table below to complete the probability density function. Be certain to list the values of XX in ascending order.

Value of X	Probability

Answer 1

Outcome Probability XX

HHH 0.3 x 0.3 x 0.3 4 x 3 - 2 x 0 = 12

HHT 0.3 x 0.3 x 0.7 4 x 2 - 2 x 1 = 6

HTH 0.3 x 0.7 x 0.3 4 x 2 - 2 x 1 = 6

HTT 0.3 x 0.7 x 0.7 4 x 1 - 2 x 2 = 0

THH

THT

TTH

TTT

Try and fill out the other probabilities, and XX values, then for each XX value add up the probabilities for that XX value