Written Problem 4: The gamma function which relates to probability and statisticsis defined as:T(x)= [ t*e"dt .You may take it without proof that this improper integral converges when x ispositive. Now, prove that:а) Г() -1b) T(x+1)=x[(x) (Hint: Write the improper integral as a limit and use IbP).c) Using a) and b), show in a few lines that I(5)=4!, and briefly explain howthe same reasoning would show that (n)=(n-1)! for any positive integer n.

use the theory of Gamma function Mathematical Property.

Written Problem 4: The gamma function which relates to probability and statistics is defined as: I(x)= [ r*e*dt. You may take it without proof that this improper integral converges when x is positive. Now, prove that: а) Г() 31 b) T(x+1)=x[(x) (Hint: Write the improper integral as a limit and use IbP). c) Using a) and b), show in a few lines that T(5)=4!, and briefly explain how the same reasoning would show that I(n)=(n-1)! for any positive integer n.

Written Problem 4: The gamma function which relates to probability and statistics is defined as: I(x)= [ redt. You may take it without proof that this improper integral converges when x is positive. Now, prove that: а) Г() 31 b) T(x+1)=x[(x) (Hint: Write the improper integral as a limit and use IbP). c) Using a) and b), show in a few lines that T(5)=4!, and briefly explain how the same reasoning would show that I(n)=(n-1)! for any positive integer n.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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