To control the quality of a manufactured product, samples of the product are taken at specified inspection time periodsand a quality characteristic is measured for each product. If the averagemeasurement falls below a certain predetermined threshold, the processis declared out of control and is interrupted. The number of inspectionsbetween successive interruptions of the process is called a run length. The expected value of the random variable X: run length is called the average run length. Suppose the probability that an inspection will result in the process being interrupted is 0.01. a. The random variable X is (choose one)
1. binomial
2. hypergeometric
3. negative binomial
4. Poisson.

b. Give the sample space and PMF of X.
c. What is the average run length?