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Question

If a random variable X follows a binomial distribution with mean 3 and variance 3/2, find P (X ≤ 5).

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Solution

Mean(np) =3 and variance (npq)=32 q=12and p =1-12n=Meanp n=6

Hence, the distribution is given by P(X=r) = Cr612r126-r , r=0,1,2...6= Cr626 P(X5) = 1-P(X=6) = 1-164=6364

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