Q.5.35 - A First Course in Probability

Question

The lung cancer hazard rate$\lambda \left(t\right)$ of a $t$-year-old male smoker is such that

$\lambda \left(t\right) = .027 + .00025{(t - 40)}^2$$t\ge 40$

Assuming that a $40$-year-old male smoker survives all other hazards, what is the probability that he survives to

$\left(a\right)$age$50$ and $\left(b\right)$age 60 without contracting lung cancer?

Step-by-Step Solution

Answer

$t=50\Rightarrow \lambda \left(50\right)=0.052$

$t=60\Rightarrow \lambda \left(60\right)=0.127$

Step 1 Given Information.

$\lambda \left(t\right) = .027 + .00025{(t - 40)}^{2 }t \ge 40$

Part a Step 2 Explanation.

$t=50,$

$\lambda \left(50\right)=0.027+0.00025{(50-40)}^2$

          $$\begin{gathered} =0.027+0.025 \\ =0.052 \end{gathered}$$

Part b Step 3 Explanation.

$$\begin{gathered} t=60, \\ \lambda \left(60\right)=0.0027+0.000259{(60-40)}^2 \end{gathered}$$

          =0.127