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__.

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By binomial distribution function-
Var(X)=npq=1.2
and E(X)=2=np
Here, p=1-q
By solving both equation-
p=0.4 , q=0.6 and n=5
Now,
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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