Random variables X and Y have joint PDFf_{X,Y}(x,y)=\begin{cases}12e^{-(

York

York

Answered question

2021-11-07

Random variables X and Y have joint PDF
fX,Y(x,y)={12e(3x+4y), x0,y00, otherwise
Find P[X+Y1]

Answer & Explanation

ensojadasH

ensojadasH

Skilled2021-11-08Added 100 answers

The value of P[X+Y1] is obtained as given below:
f(x,y)=12e(3x+4y);x0andy0
f(x)=yf(x,y)dy
=012e(3x+4y)dy
=12e3x[e4y4]0
=12e3x×14
f(x)=3e3x
P(X+Y1)=P(X1Y)
=01yf(x)dx
=01y3e3xdx
=3[e3x3]01y
=[e3(1y)1]
=[1e3(1y)]

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