A coin is flipped twice. Let Y = number of heads obtained, when the probability of a head for a flip equals p.
a. Assuming p = 0.50, specify the probabilities for the possible values for Y , and find the distribution's mean and standard deviation.
b. Find the binomial probabilities for Y when p equals (i) 0.60, (ii) 0.40.
c. Suppose you observe y = 1 and do not know p. Calculate and sketch the likelihood function.
d. Using the plotted likelihood function from (c), show that the ML estimate of p equals 0.50.