Question

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?

Answer 1

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