Question

For the experiment, flip a coin until heads shows, assume that the probability of heads on one flip is 3
5
.
We define a RV X = the number of flips.
1. What are the possible values of X?
2. Find the probability distribution function for X: give the first four values, and then find a general
formula for the probability that X = n
3. Prove that the sum of all the probabilities is 1 using the formula for the sum of a geometric series.
4. Find the probability that X will be no more than 10. You may find it helpful to use the formula for a
partial sum of a geometric series