A frog is trapped in a well. In order to escape from the well the frog needs to climb up three steps. The frog can jump high enough for one step at a time. However, it needs to jump at a certain angle inorder to land on the next step successfully. Each time it jumps it successfully jumps to the next step with probability q. Otherwise, it hits the vertical side of the stair and bounces back to where it was with probability 1-q and tries again starting from the same step. Let X denote the number of jumps the frog makes before it escapes the well.

a. What is the probability mass function (PMF) of X?
b. Compute E [X].
c. Suppose that the frog escaped from the well after four jumps. Given this, what is the probability that the first jump was successful, i. e., the frog moved on to the first step from the bottom after the first jump?