Q6, Chapter 5, Introduction to probability, Blitzstein, Please solve this question:

6. The 68-95-99.7% rule gives approximate probabilities of a Normal r.v. being within

1, 2, and 3 standard deviations of its mean. Derive analogous rules for the following

distributions.

(a) Unif(0, 1).

(b) Expo(1).

(c) Expo(1/2). Discuss whether there is one such rule that applies to all Exponential

distributions, just as the 68-95-99.7% rule applies to all Normal distributions, not just

to the standard Normal.