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Question

Mathematics Question on Sequence and series

In a binomial distribution, the mean is 23 and variance is 59. What is the probability that random variable D=2?

A

(A) 536

B

(B) 2536

C

(C) 2554

D

(D) 25216

Answer

(D) 25216

Explanation

Solution

Explanation:
Concept:Mean = npVariance = npqWhere n is the total number of cases, p is probability of favorable cases and q is probability of unfavorable cases(1 - p)Given mean =np=23… (i)And variance =npq=59… (ii)On dividing equation (i) and (ii) variance mean =5923q=56p=1−q=16np=23n=4∴ The probability that random variable D=2P=nC2 p2qn−2P=4C2×(16)2×(56)2P=6×136×2536P=25216Hence, the correct option is (D).