Question: Using the properties of the gamma function, show that the gamma PDF integrates to 1, i.e., show that for , > 0, we have Xx-e-x

Using the properties of the gamma function, show that the gamma PDF integrates to 1, i.e., show that for α,λ > 0, we haveXx-e-x r(a) So dx = 1.

Xx-e-x r(a) So dx = 1.

Step by Step Solution

★★★★★

3.52 Rating (155 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

We can write S Xx1p... 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

Students Have Also Explored These Related Introduction To Probability Statistics Questions!

Q:

Below are three independent lease scenarios. Payments are made at the beginning of each year. Case 1 Case 2 Case 3 Fair value of equipment $ 160,000 $ 95,000 $ 125,000 Unguaranteed residual value...

Q:

The following proof that the normal pdf integrates to 1 comes courtesy of Professor Robert Young, Oberlin College. Let f(z) denote the standard normal pdf, and consider the function of two variables...

Q:

A firm is considering two different financing capital structures (CS1 and CS2). In the first capital structure CS1 the firm will issue equity which will pay expected dividends of $2 million every...

Q:

Using the properties of water at the triple point, develop an equation for the saturation pressure along the fusion line as a function of temperature.

Q:

1. Calculate the sample size needed given these factors: one-tailed t-test with two independent groups of equal size small effect size (see Piasta, S.B., & Justice, L.M., 2010) alpha =.05 beta = .2...

Q:

Probability and Statistics - Problem Set c Keith M. Chugg October 2, 2015 1 Preliminaries, Combinatorics, Set Probability 1.1. A number of bats are in a cave. 2 bats can see out of their left eye. 3...

Q:

Applied Mathematics and Computation 95 (1998) 181192 Love dynamics: The case of linear couples Sergio Rinaldi 1 Centro Teoria dei Sistemi, CNR, Politecnico di Milano, Via Ponzio 34/5, 20133 Milan,...

Q:

nodes, but at least its bias can be quantified by Markov Chain L. INTRODUCTION analysis and thus can be corrected via appropriate re-weighting The popularity of online social networks (OSNs) in...

Q:

Stat 110 Homework 7, Fall 2015 Due: Friday 11/6 at 12:01 pm. Handwritten homework must be turned in on paper. If you hand-write your homework, please turn it in at the Stat 110 dropbox (outside SC...

Q:

Describe the meaning of the results and how they answer the research question? An ANOVA approach for accounting for life-cycle uncertainty reduction measures in RBDO: the FSAE brake pedal case study...

Q:

Tactics Mentioned? Sample Size (n): ? Number of Groups: ? Number of Treatments: ? Standard Deviation ():? Standard Error:? Mean (): ? F Statistic: ? Degrees of Freedom (df):? P-Value:? An ANOVA...

Q:

Mercedes-Benz is thinking about advertising its cars to college students. Do you think that college students are a viable potential market for Mercedes? Why or why not?

Q:

Obtain from your library a copy of following article: Clayton M. Christensen, Stephen P. Kaufman, and Willy C. Shih, Innovation Killers: How Financial Tools Destroy Your Capacity to Do New Things,...

Q:

What is the difference between excess demand and excess supply?

Q:

Briefly explain the term marketing concept, and provide an illustration of how it is applied. (LO3)

Q:

If height is normally distributed with a mean of 68 inches and a standard deviation of 5 inches, what is the probability of selecting someone who is 70 inches or taller?

Q:

For the distribution described in exercise 4, what is the probability of selecting someone who is 64 inches or shorter? Data from exercise 4 If height is normally distributed with a mean of 68 inches...

Q:

For the distribution described in exercise 4, what is the probability of selecting someone who is 70 inches or taller or 64 inches or shorter? Data from exercise 4 If height is normally distributed...

Q:

Shown below are next years budgeted operating costs for Fibre Ltd, a company with three production and twoservice departments. Production departments Service departments Total Weaving dept Proofing...

Q:

This lab has you using composition on the Name and PhoneNumber classes of the previous two labs to create a third, more complex class named PhonebookEntry. The basic structure is the same only now...

Q:

Scheme. Hello I am trying to rewrite this function to be tail recursive. (define (decode bits tree) (define (decode-1 bits current-branch) (if (null? bits) '() (let ((next-branch (choose-branch (car...