1.Let be a random variable having the distribution as follows:

Let .

a.Solve the following problems;

i.Verify whether and are one-to-one relationship.

ii.Find .

iii.Find the domain of .

b.From (a) obtained, state the probability density function of .

c.Find the moment generating function of .

d.Let = 5 and = 2, by using (c), find the mean and variance of .

e.Let and has the relationship and is defined as follows,

and has the distribution probability density function follows,

Find ().