(ASV Exercise 5.21) Let X be a random variable with moment generating function M
X
​
(t). Let us consider a new random variable Y=aX+b, for some real numbers a,b. Write the moment generating function M
Y
​
(t) of Y in terms of M
X
​
(t). Hint: use the definition of M
X
​
(t) and properties of the expectation. (ASV Exercise 5.31) Suppose that U∼Unif[0,1]. Let Y=e
1−U
U
​

. find the probability density function of Y.