Question

For the hazard rate function λ(t) = 1 + 0.5 t + 10/t, t ≥ 1,...

For the hazard rate function λ(t) = 1 + 0.5 t + 10/t, t ≥ 1, plot both λ(t) and f(t).

Math   Statistics-And-Probability   
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Homework Answers

Answer #1

The CDF F(t) is given as,

(The limits of integration is from 1 to t as t ≥ 1)

Using below R code, the plot is generated.

t = seq(1,10, by = 0.05)
lambda = 1 + 0.5 * t + 10/t
op <- par(mfrow=c(2,1),mar=c(4,4,2,1))
plot(t, lambda, type = "l", ylab = "lambda")
ft = (1 + 0.5 * t) * exp(-t - 0.25 * t^2 + 1.25) + t^(-9)/9
plot(t, ft, type = "l", ylab = "f(t)")

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