The factorial moment-generating function

Assignment Help Basic Statistics

Reference no: EM131129241

The factorial moment-generating function of a discrete random variable X is given by

Show that the rth derivative of F_X(t) with respect to t at t = 1 is μ'_(r), the rth factorial moment defined in Exercise 11.

In the proof of Theorem 2 we determined the quantity E[X(X - 1)], called the second factorial moment. In general, the rth factorial moment of X is given by

Express μ'₂, μ'₃, and μ'₄ in terms of factorial moments. 1

Theorem 2

The mean and the variance of the binomial distribution are

Reference no: EM131129241

Questions Cloud

The mean and the variance of the binomial distribution : In the proof of Theorem 2 we determined the quantity E[X(X - 1)], called the second factorial moment. In general, the rth factorial moment of X is given by

Describe five additional relationships that might be useful : Describe five additional relationships that might be useful in the context of an SCM repository

What is the expected utility from this prize : What is the minimum payment that Connie will accept to forego the roll of the dice - What is the expected utility from this prize?

What is the current market price of the bonds : Jackson Corporation's bonds have 6 years remaining to maturity. Interest is paid annually, the bonds have a $1,000 par value, and the coupon interest rate is 7.5%. What is the current market price of these bonds?

The factorial moment-generating function : In the proof of Theorem 2 we determined the quantity E[X(X - 1)], called the second factorial moment. In general, the rth factorial moment of X is given by

How much could sandra increase her expected utility : How much could Sandra increase her expected utility if she read and believed the weather report?

What is the change in the bank capitalization ratio : Springer County Bank has assets totaling $180 million with a duration of five years, and liabilities totaling $160 million with a duration of two years. If interest rates drop from 9% by 75 basis points, what is the change in the bank’s capitalizatio..

The main tenets of measurement theory : write a brief paper that outlines the main tenets of measurement theory. Individual project: Develop a presentation on the subject and present it to your class.

Calculate the change in the market value of assets : Calculate the change in the market value of assets and liabilities when the average duration of assets is 3.60, the average duration of liabilities 0.88, and interest rates increase from 5% to 5.5%.

User Account

All Pages