GATE 2020 ST – Question 54
The joint MGF is $M_{X,Y}(s,t)=e^{2s^2+t}$. Let $p=P(X+2Y<1)$. Given Φ(0) = .5, Φ(.5) = .6915, Φ(1) = .8413 and Φ(1.5) = .9332, find 2p+1 to two decimal places.
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Correct answer: 1.61 to 1.63
Explanation
The factor e^(2s²) is the MGF of N(0,4), while eᵗ means Y=1 almost surely. Thus p=P(X<−1)=Φ(−0.5)=1−0.6915=0.3085. Therefore2p+1=1.617, or1.62.