Let p be the probability of getting a Tail when a particular coin is tossed (you should assume that outcomes of different tosses are independent). In an experiment this coin is to be tossed 20 times, and X is defined as the total number of tails observed. We have resources to repeat the above experiment 5 times. Let X1, X2, X3, X4, X5 denote the outcomes for the 5 experiments. Required:
a. Write the joint probability mass function for X1, X2, X3, X4, X5.
b. Assume that Xi = 5, X2 = 14, X3 = 8, X. = 10, X5 = 4. Calculate the value of p, that minimizes the above function at the current observed values of X;'s.