Suppose that X and Y are continuous random variables with joint pdf f(x,y)=e^{-(x+y)} 0<x<\infty\ and\ 0<y<\infty and zero otherwise.Find P(X>3)

nagasenaz

nagasenaz

Answered question

2021-05-23

Suppose that X and Y are continuous random variables with joint pdf f(x,y)=e(x+y)0 and zero otherwise.
Find P(X>3)

Answer & Explanation

Arnold Odonnell

Arnold Odonnell

Skilled2021-05-24Added 109 answers

Step 1
Introduction:
The joint density function of two random variables X and Y is given below:
f(x,y)={e(x+y).   0x,0y<0. elsewhere}
The marginal density function of X is,
f(x)=0e(x+y)dy
=ex0eydy
=ex[ey]0
=ex[ee0]
=ex[0,1]
=ex
Step 2
The probability of P(X>3) is obtained as 0.0498 from the calculation given below:
P(X>3)=3exdx
=[ex]3
=[ee3]
=[0e3]
=e3
=0.0498
Thus, the probability of P(X>3) is 0.0498.

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