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Q5 An electronic device consists of two components. Let

`x`

and

`Y`

[years] be the times to failure of the first and second components, respectively. Assume that

`(x,Y)`

has the density

`f(x,y)=4e^(-2(x+y))`

if

`x,y`

both are

`>0`

and 0 otherwise. (a) Are

`x`

and

`Y`

dependent or independent? (b) Find the densities of the marginal distributions. (c) What is the probability that the first component will have a lifetime of 2 years or longer?