We model the following coin toss experiment. Toss a coin n times. Let A1, A2, An that X₂ = 1 if ith coin toss lands on head; otherwise X₂ = 0, i = 1, ..., n. Then each X, is a Bernoulli random variable with distribution function f(X) = px (1 - p)1-X₁, where the unknown parameter p = Pr(X; = 1), i=1,...,n. We aim to make inference of the unknown parameter p, the probability of getting a head, based on the data X₁,..., Xn. a. Find the joint distribution f(X1,..., Xn) of the data X₁,.., Xn. b. Find the log-likelihood function of p based on the result of a. c. Find the maximum likelihood estimator (MLE) of p based on the result of b.

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A: Dear student, If you find this solution helpful please upvote it. The solution is given below :

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