Question

2. Show that the first derivative of the the moment generating function of the geometric evaluated at 0 gives you the mean.

3. Let X be distributed as a geometric with a probability of success of 0.10.

a. Give a truncated histogram (obviously you cannot put the whole sample space on the x-axis of the histogram) of this random variable.

b. Give F(x)

c. Find the probability it takes 10 or more trials to get the first success.

d. Here is a challenge. What is the probability that it takes an even number of trials to get the first success, i.e., P(X=2,4,6,8,...)

Answer 1