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Let {Xi, i ≥ 1} be independent and identically distributed random variables with P(Xi = 1) = p = 1 - P(Xi = 0), Sn\(\sum^n_i{_=}{_1}\) Xi . The distribution of Sn is:
1. Geometric distribution with parameter p
2. Bernouli distribution with parameter p
3. Binomial distribution with parameter n and p
4. Bernoulli distribution with parameter np

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Correct Answer - Option 3 : Binomial distribution with parameter n and p

Explanation:

Let {Xi, i ≥ 1} be independent and identically distributed random variables with P(Xi = 1) = p = 1 - P(Xi =0), Sn = \(\sum^n_i{_=}{_1}\) Xi . The distribution of Sn is :

Binomial distribution with parameter n and p

1 - Suppose a discrete random variable X has the following pmf P(X = k) = qk P, 0 ≤ k < ∞ The X is said to have Geometric distribution with parameter p

2 - A discrete random variable X is said to follow Bernoulli distribution with parameter p if its probability mass function is given by

,P[X = x] = {px(1 - p)1 -x  x = 0,1 and 0, elsewhere

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