Chapter 12.4, Problem 14E

(a)

To determine

To prove: $S\left(x\right)=1-F\left(x\right)$, where $S\left(x\right)$ is the survival function and $F\left(x\right)$ is the cumulative distribution function of $X$ and compute $S\left(x\right)$.

(b)

To determine

The constant $k$ in the exponentialdensity function $f\left(x\right)$, where the probability that the patient will survive at least $5$ years is $S\left(5\right)=0.90$.