14.2 Exercise 29

Time to failure X of a manufactured unit has an exponential distribution. The parameter is dependent upon the manufacturing process. Suppose the parameter is the value of random variable $H \sim$ uniform on[0.005, 0.01], and X is conditionally exponential $\left(u\right)$, given $H = u$. Determine $P \left(X > 150\right)$. Determine $E \left[\right. X \left|\right. H = u \left]\right.$ and use this to determine $E \left[X\right]$.