Let Xi be an absolutely continuous random variable having the probability density function
\(f_i(x)=\left\{\begin{array}{cl} i e^{-i x}, & \text { if } x \geq 0 \\ 0, & \text { if } x<0 \end{array}, \right.\)i = 1, 2 .
Consider a series system comprising of independent components having random lifetimes described by random variables X1 and X2. Let X denote the lifetime of the series system. Then which of the following statements are true?
1
P(X > 4) = P(X > 1) P(X > 2)
2
P(X > 4| X > 2) = P(X > 2)
3
\(E(X)=\frac{1}{3} \)
4
\(6 X \sim \chi_3^2\)