Random variables X and Y have joint PDF f_{X,Y}(x,y)=\begin{cases}12e^{-(3x+4y)},\ x \geq 0, y \geq 0\\0,\ otherwise\end{cases} Find P[max(X,Y)\leq 0.5]

OlmekinjP 2021-05-30 Answered
Random variables X and Y have joint PDF
fX,Y(x,y)={12e(3x+4y), x0,y00, otherwise
Find P[max(X,Y)0.5]
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Expert Answer

pattererX
Answered 2021-05-31 Author has 95 answers

The value of P[max(X,Y)0.5] is obtained as given below:
P[max(X,Y)0.5]=P(X0.5,Y0.5)
=P(X0.5)×P(Y0.5)
P(X<0.5)=00.53e3xdx
=3[e3x3]00.5
=1e1.5
=0.7769
P(Y<0.5)=00.54e4ydy
=4[e4y4]00.5
=1e2
=0.8647
P[max(X,Y)0.5]=P(X0.5)×P(Y0.5)
=07769×0.8647
=0.6718

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