(Answered) Question there are two coins one with probability p1 of

Statistics

Question: There are two coins, one with probability p₁ of Heads and the other with probability p2 of Heads. One of the coins is randomly chosen (with equal probabilities for the two coins). It is then flipped n ≥ 2 times. Let X be the number of times it lands Heads.

(a) Find the PMF of X.

(b) What is the distribution of X if p₁ = p₂?

(c) Give an intuitive explanation of why X is not Binomial for p₁ ≠ p₂ (its distribution is called a mixture of two Binomials). You can assume that n is large for your explanation, so that the frequentist interpretation of probability can be applied.

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