A random variable X ∽ B ( n , p ) . If values of mean and variance of X are 18 and 12 respectively then total number of possible values of X are

Question

A random variable X ∽ B ( n , p ) . If values of mean and variance of X are 18 and 12 respectively then total number of possible values of X are, 54, 55, 12, 18

MARKS App · Accepted Answer

Mean = np = 18 Variance = npq = 12 ⇒ n p q n p = 12 18 ⇒ q = 2 3 ⇒ p = 1 - q = 1 - 2 3 ⇒ p = 1 3 Now n p = 18 ⇒ n 1 3 = 18 ⇒ n = 54 ⇒ ∴ Values of X are 0, 1, 2, ........... 54 ∴ 55 Values.

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