Let X₁,..., X5 be a random sample from a Bernoulli distribution with parameter p and let the prior distribution have a Beta distribution with the pdf f(x; a) = 6x(1 - x) for 0< x < 1, and zero otherwise. If the sum of the observed sample is 3 (i.e., ₁ į = 3 ), which statement is correct? i=1 (1) The posterior distribution has a Beta distribution with parameters 5 and 4 respectively. (II) The posterior distribution has a Beta distribution with parameters 4 and 5 respectively. (III) The posterior distribution has a Beta distribution with parameters 4 and 3 respectively. (IV) The posterior distribution has a Beta distribution with parameters 3 and 4 respectively. (11) O (1) O (III) O (IV)

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