1. The problem statement, all variables and given/known data
A machine consists of 2 components whose lifetimes are X and Y and have joint pdf,
[tex] f(x,y)=1/50[/tex] w/ [tex]0<x<10[/tex], [tex]0<y<10[/tex],[tex]0<x+y<10 [/tex]
Calculate the expected value of [tex]X [/tex] given [tex]Y=5[/tex].
2. Relevant equations
[tex]E[X|Y]= \int_{-inf}^{inf} x f(x,y)/f(y) dx[/tex]
3. The attempt at a solution
[tex]f(y) = \int_{0}^{10-y} 1/50 dx = (1-y)/5[/tex]
[tex]E[x|y] = \int_{0}^{10-y} x/(10-10y) dx [/tex]
This is where I am confused. How do i set the limits on the integral where I actually compute the expectation? Is x=0 to x=10-y right? I was thinking I want to just integrate as normal and plug in y=5 after the integration.
A machine consists of 2 components whose lifetimes are X and Y and have joint pdf,
[tex] f(x,y)=1/50[/tex] w/ [tex]0<x<10[/tex], [tex]0<y<10[/tex],[tex]0<x+y<10 [/tex]
Calculate the expected value of [tex]X [/tex] given [tex]Y=5[/tex].
2. Relevant equations
[tex]E[X|Y]= \int_{-inf}^{inf} x f(x,y)/f(y) dx[/tex]
3. The attempt at a solution
[tex]f(y) = \int_{0}^{10-y} 1/50 dx = (1-y)/5[/tex]
[tex]E[x|y] = \int_{0}^{10-y} x/(10-10y) dx [/tex]
This is where I am confused. How do i set the limits on the integral where I actually compute the expectation? Is x=0 to x=10-y right? I was thinking I want to just integrate as normal and plug in y=5 after the integration.
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