An experiment involving n independent trials with success probability p is repeated 4 times. The following number of successes during each set of trials is listed below:
Number of successes: 6, 5, 9, 7
a. If the number of trials during each experiment is 12, determine the maximum likelihood estimate for the probability of success, p.
b. Repeat part (a) if we know that the success probability must be either 0.5 or 0.75.
c. If we know the probability of success is 0.8, determine the maximum likelihood estimate for the number of trials in each experiment, n.