GATE 2021 ST – Question 26

Probability · Random Variables and Transforms · 1 mark · Numerical answer

X has CDF 0 for x<1,a/2 for 1≤x<2,c/6 for 2≤x<3,and 1 for x≥3. Let A_n=[1+1/n,3−1/n] and A=⋃_(n≥1)A_n. Given P(X≤1)=1/2 and E X=5/3,find P(X∈A),to two decimals.

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Correct answer: 0.32 to 0.35

Explanation

The union is (1,3),so only the atom at 2 contributes. P(X=1)=1/2. If p=P(X=2),then P(X=3)=1/2−p. The mean is 1/2+2p+3(1/2−p)=2−p=5/3,so p=1/3. Answer **0.33**.

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