Let X1, X2 denote lifetimes (in years) of 2 components of an electronic system. Let Y1 = X1 + X2, Y2 = max{X1, X2} and Y3 = min{X1,X2}. Assume that X1 and X2 are independent, each following exponential distribution with probability density function \(\rm f(x)=\left\{\begin{matrix}\frac{1}{2}e^{-x/2},&if\ x>0\\\ 0, &otherwise\end{matrix}\right.\)
Which of the following statements are true?
1
P(Y1 > 2) = 2e-1
2
P(Y2 > 2) e-2
3
P(Y3 > 2) = e-2
4
Var(Y1 + Y2 + Y3) = 32