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) e x for some positive value of , defined for x 0 For each of the following values of , a Find the c d f b Plot the p d f and c d f c Check that t...

a The cdf is b c G x 0 05e 05 x 05e 05 x ...

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

Question:

α = 0.5. The p.d.f. for the waiting time X until an event occurs often follows the exponential (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. Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...