3.9 moment generating functions

Question 1

how to calculate m(t)

Answer 1

calculate E(e^ty) = m(t) thus expected value of function for discrete distibutions of y sum over the entire range of y with sigma

Question 2

how to use m(t)

Answer 2

getting first dirivitive in regards to t and setting t = 0 is the first moment taken about the origin and is equal to the mean and second sentral moment is E(Y^2)

Question 3

generised use of m(t)

Answer 3

calculating the kth dirivitive and setting t = 0 will yeild the kth central moment around the origin

Question 4

Transformative moment generating functions U = ay +b and the moment generating function of y is know what is moment generating of U

Answer 4

e^tb*m(at) and then work in all values of a into original moment generating function