GATE 2022 ST – Question 25

Standard Univariate Distributions · Continuous Distributions · 1 mark · Numerical answer

X,Y are independent exponential variables with E X²=1/2 and E Y²=2/9. Find P(X<2Y) to two decimals.

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Correct answer: 0.55 to 0.59

Explanation

For exponential rate r,the second moment is 2/r². Thus rates are r_X=2,r_Y=3;2Y has rate 3/2. For independent exponential waits,P(X<2Y)=2/(2+3/2)=4/7≈**0.57**.

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