2. Use t=read.table(”RobotReactTime.txt”, header=T);

t1=t$Time[t$Robot==1] to import the data on robot reaction times to simulated malfunctions, and copy the reaction times of Robot 1 into the R object t1.

(a) Follow the approach of Example 6.3-3 to fit the Weibull(α, β) model to the data in t1. (Hint. Use mean(t1); var(t1) to compute the sample mean and variance.)

(b) Use Example 6.3-5 to fit the exponential(λ) model to the data in t1.

(c) Use each of the fitted models in parts

(a) and (b)

to give model-based estimates of the 80th population percentile of reaction times, as well as the probability P(28.15 ≤ X ≤ 29.75), where X denotes the next response time of Robot 1. (Hint. See Example 6.2-5.)

(d) Give empirical estimates for the 80th population percentile and the probability P(28.15 ≤ X ≤ 29.75). (Hint. The R command for finding percentiles is given in Section 1.7. The R command sum(t1>=28.15&t1<=29.75) counts the number of reaction times that are between 28.15 and 29.75.

Finally, length(t1) gives the number of observations in t1.)