Suppose X ∼ Binomial(50, p), and we make the observation X = x. Say whether each of the following statements is true or false. If the statement is false, explain why.

a. The maximum likelihood estimate is the parameter value p under which the observed data x is as likely as possible.

b. The maximum likelihood estimate is the observation x that is most likely under the given parameter value p.

c. Maximum likelihood estimation is about finding the value p that is the most statistically significant out of all possible values of p.

d. The likelihood function has the same formula as the probability function, but is expressed as a function of p instead of a function of x.