Suppose we roll a fair die and let x represent the number on the die. (a) find the moment generating function of x. (b) use the moment generating function to find the first two moments. that is, find e[x] and e[x2 ].

(a)  moment generating function for X is

(b)

Step-by step explanation:

Given X represents the number on die.

The possible outcomes of X are 1, 2, 3, 4, 5, 6.

For a fair die,

(a) Moment generating function can be written as .

(b) Now, find using moment generating function

Hence, (a) moment generating function for X is .

(b)

45

step-by-step explanation: