please be detailed,!

A quality control manager wants to estimate the probability that an item being produced by an automatic process is defective. She devises the following sampling procedure: once every hour during an 8-hour day she samples sequential items coming off the assembly line and inspects the items until she finds a defective one. The random variable X = the first choice on which she observes a defective item. For example if she sees the sequence GOOD, GOOD, GOOD, DEFECTIVE, then X = 4. X has a Geometric Distribution P(X = xi) = p(1 p)xi_1, where p = probability that an item is good. On one day the 8 hourly readings are {3, 2, 4, 1, 2, 2, 5, 3}. Based on these values the likelihood function for the probability of a defective item is a multiple of: O None of the other choices is correct np14(1_p)8