3. A device runs until either 2 components fails, at which the device stops running. Let...

3. A device runs until either 2 components fails, at which the device stops running. Let X and Y be the lifetimes in hours of the first and second component, respectively. The joint probability density function of the lifetimes is:

f(x,y) = { (x+y)/27 : 0 < x < 3, 0< y < 3

{ 0

a) Find the marginal probability density function of X and the marginal probability density function of Y.

b) Are X and Y independent? Why or why not?

c) Find the conditional density of X given that Y = y

d) Find the expected value of X given that Y =1/4

Please show your work, I have an exam tomorrow, thank you!

Expert Solution

milcah answered 5 days ago

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