GATE (TF) Textile 2018 Question Paper Solution | GATE/2018/TF/40

Question 40 (Textile Technology & Fibre Science)

Let X be a random variable following the binomial distribution. If E(X)=2 and Var(X)=1.2, then P(X=2), accurate to three decimal places, is equal to __0.325 to 0.365__.

Answer / Solution

By binomial distribution function-
and E(X)=2=np
Here, p=1-q
By solving both equation-
p=0.4 , q=0.6 and n=5
P(x=2)=n_c_r \times p^r \times q^(n-r)
P(r=2)=5_c_2 \times (0.4)^2 \times (0.6)^(5-2)
P(r=2)=5_c_2 \times (0.4)^2 \times (0.6)^(3)
P(X)=0.3456 (Ans)

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