Question: Use the moment-generating function of a gamma distribution to show that E(X) = and Var(X) = 2

Use the moment-generating function of a gamma distribution to show that
E(X) = αθ and Var(X) = αθ2

Step by Step Solution

★★★★★

3.49 Rating (162 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

The moment generating function ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

579-M-S-D-D (631).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

Now use the moment generating function from Exercise 43.13 to verify that, if X is Gamma with parameters , r, then E(X2) = r(r + 1)/2.

Q:

Use the moment generating function from Exercise 1 to verify that, if X is Geometric with parameter p, then E(X) = 1/p. In Exercise 1 P(X = x) = px(x) = (1- p)x-lp For x = 1, 2, 3,..., and pX(x) = 0...

Q:

Now use the moment generating function from Exercise 43.1 to verify that, if X is Geometric with parameter p, then E(X2) = (2 - p)/p2. In Exercise 1 P(X = x) = px(x) = (1- p)x-lp For x = 1, 2, 3,...,...

Q:

Please write the code in PYTHON and show the full code. Thanks! In this exercise we will compare numpys computing time to make an array (list) to Pythons computing time using list comprehension...

Q:

(a) Find the moment-generating function for a gamma probability distribution with parameter a > 0 and > 0. (b) Using the mgf of a gamma probability distribution, find E (X) and Var (X).

Q:

Given, .... an follows poission and the prior is Gamma (ox, $). then the posterior also follows Gamma distribution with parameters. ' = sum of x : and B's B3 hB+1 ( x , B ) = ( 2, 1/ 4 ) Thus, in...

Q:

The following Bayesian Network represents two causes and two effects related to Lung Cancer. Each variable takes the value true (t) or false (f). We will abbreviate the five variable names using...

Q:

Computers For All Sdn Bhd (CFA), a Malaysian resident company, is in the business of manufacturing computer parts. The company's income statement for the year ended 31 May 2021 is as follows: Note...

Q:

Value at risk (VaR) Year 1989 1990 1991 1992 1993 1994 1995 1996 1997 1998 1999 2000 2001 2002 2003 2004 2005 2006 2007 2008 Average Standard Deviation VaR(5%) Large Stocks Returns (%) 19.21 -10.80...

Q:

Question 2 (20 points) Let X, X,,.., X be iid observations from a Bernoulli( p) distribution, the pdf of X is given by f(x; p) = p*(1- p)" * for xe {0, 1) a) Use the moment-generating function (mgf)...

Q:

A Company is trading in a fully depreciated old asset for a new one. Cost of the new asset is $10000 with a 5-year life and straight-line depreciation will be used. The company receives a $500...

Q:

Exercise 11-3 Exercise 11-5 Discussion Question This chapter focuses on equity analysis and valuation. Specifically, the module focuses on earnings persistence and earnings power. For this discussion...

Q:

18. NRF/BIG research provided results of a consumer holiday spending survey (USA Today, December 20, 2005). The following data provide the dollar amount of holiday spending for a sample of 25...

Q:

What are the measures to judge the success of trade fair participation?

Q:

If 3 books are picked at random from a shelf containing 5 novels, 3 books of poems, and a dictionary, what is the probability that (a) The dictionary is selected? (b) 2 novels and 1 book of poems are...

Q:

In a poker hand consisting of 5 cards, find the probability of holding (a) 3 aces; (b) 4 hearts and 1 club.

Q:

In a game of Yahtzee, where 5 dice are tossed simultaneously, find the probability of getting 4 of a kind.

Q:

Drogo, Inc., is trying to determine its cost of debt. The firm has a debt issue outstanding with 14 years to maturity that is quoted at 105 percent of face value. The issue makes semiannual payments...

Q:

A door delivery florist wishes to estimate the proportion of people in his city that will purchase his flowers. Suppose the true proportion is 0.07. If 209 are sampled, what is the probability that...

Q:

Hacker Software has 9.4 percent coupon bonds on the market with 19 years to maturity. The bonds make semiannual payments and currently sell for 107.5 percent of par. a.) What is the current yield on...