Rework problem 1 in section 4.1 of your text, involving the flipping of a loaded coin, but assume that Pr[H] = 0.3. Also, assume that the coin is flipped 4 times, and the random variable X is defined to be 3 times the number of heads minus 2 times the number of tails ... How many different values are possible for the random variable X?

As you must be knowing, the formula for x successes in n trials in a binomial distribution where p is the probability of a success in a single trial & q = 1 - p is the probability of failure in a single trial is

P (x) = nCx*p^x*q^n-x

For this problem, what you have to do is to find

x*P (x) for all values of x from 0 to 15, using

p = 0.3 & q = 4/5, i. e

0*P (0) + 1*P (1) + ... 15*P (15) =

0*15C0 * (0.3) ^0 * (4/5) ^15 + 1*15C1 * (0.3) ^1 * (4/5) ^14 + ...

15*15C15 * (o. 3) ^15 * (4/5) ^0