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Chapter 4: Q.4.9 (page 173)

If X is a binomial random variable with expected value 6and variance2.4, find P{X=5}

Short Answer

Expert verified

P(X=5)=0.2

Step by step solution

01

Step 1: Given information

Given in the question that,Xis a binomial random variable with expected value6and variance 2.4,

02

Step 2: Explanation

We have that X~Binom(n,p).

We are given informations

EX=6⇒np=6

Var(X)=2.4⇒np(1-p)=2.4

Dividing the second equation with the first one, we end up with equation 1-p=2.46=0.4, so we have that p=0.6. Hence, we also have that n=10.

Finally, we are required to determine following

P(X=5)=1050.650.45=0.2

03

Step 3: Final answer

P(X=5)=0.2

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