Problem: Survival function and hazard rate for the exponential distribution

Eksempel

This problem is a slightly modified version of Exercise 1.1(a) in ABG. In the problem you are given a density function and are asked to find the corresponding hazard rate and survival function.

Problem

Let \(T\) be an exponentially distributed stochastic variable, so that it density function is \[f(t) = \lambda e^{-\lambda t}, t > 0.\] Find formulas for the corresponding hazard rate and survival function. Use also R to make plots of the density function, the hazard rate and the survival function when \(\lambda = 2.0.\)

Hints: To get some hints for how to solve the problem see the link at the bottom of this page.