The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater than 1 , is

Question

The mean and variance of a binomial variable X are 2 and 1 respectively. The probability that X takes values greater than 1 , is, 5 16, 8 16, 11 16, 1 16

MARKS App · Accepted Answer

Given, mean n p = 2 ...(i) And variance n p q = 1 ...(ii) From Eqs.(i) and (ii), we get q = 1 2 ∴ p = 1 - q = 1 2 From Eq.(i), n × 1 2 = 2 ∴ n = 4 The binomial distribution is 1 2 + 1 2 4 Now, P X > 1 = P X = 2 + P X = 3 + P ( X = 4 ) = 4 C 2 1 2 2 1 2 2 + 4 C 3 1 2 3 1 2 1 + 4 C 4 1 2 4 = 6 + 4 + 1 16 = 11 16

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