= 0.5. The p.d.f. for the waiting time X until an event occurs often follows the exponential

α = 0.5. The p.d.f. for the waiting time X until an event occurs often follows the exponential distribution (to be studied in Section 7.6), with the form g(x) = αe-αx for some positive value of α, defined for x ≥ 0. For each of the following values of α,
a. Find the c.d.f.
b. Plot the p.d.f. and c.d.f.
c. Check that the p.d.f. is the derivative of the c.d.f.
d. Find Pr(X ≤ 1). Indicate this on both of your graphs.
e. Find Pr(l ≤ X ≤ 3).
f. Find Pr(l ≤ X ≤ 1.01) and show that it is approximately g(1) ∙ 0.01.