The distribution function of a random variable X is given by

for some positive constants a and k.
(i) Find the value of the probabilities P(X = 0) and P(X = a).
(ii) For what value of k, we have P(X =

a) = 1∕4?
(iii) For a = 4, k = 2, obtain the value of t such that

(Distributions of this form occur frequently in insurance modeling [the scientific area where such models are studied and used is known as actuarial science], in particular in excess of loss reinsurance; see the footnote earlier in this section.)

0, t < 0, 0t a,