(a) Consider a normal distribution with mean 100 and variance 100. Write out the CDF of the threshold exceedance distribution with respect to 120 (two standard deviations above the mean). Just use symbols for functions that cannot be evaluated in closed form.

(b) Use R or another computer program to produce a plot of the \(\mathrm{CDF}\) of the normal exceedance distribution in the previous question.

What is the probability that the random variable exceeds three standard deviations above the mean (that is, 130), given that it has exceeded the threshold?

(c) Consider a gamma distribution with shape parameter 4 and scale parameter 10 . Write out the CDF of the threshold exceedance distribution with respect to 80 (two standard deviations above the mean). Just use symbols for functions that cannot be evaluated in closed form.

(d) Use R or another computer program to produce a plot of the \(\mathrm{CDF}\) of the gamma exceedance distribution in the previous question.