Exams › SSC CGL (Prelims) › General

Suppose Y1, Y2, ..., Y10 are 10 independent and identically distributed random variables, each taking value 0 with probability q and value 1 with probability p. What is the distribution of S = Y1 + Y2 + ... + Y10?

1. a binomial variate
2. Poisson distribution
3. a normal variate
4. a geometric variate

Correct answer: a binomial variate

Solution

Each Yi follows a Bernoulli distribution with parameter p. The sum of n independent and identically distributed Bernoulli(p) random variables follows a Binomial(n, p) distribution. Here n = 10, so S ~ Binomial(10, p).

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