Let X have a gamma distribution with parameters and . Show that P(X 2)

Question:

Let X have a gamma distribution with parameters α and β. Show that P(X ≥ 2αβ) ≤ (2/e)^α.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Introduction To Mathematical Statistics

ISBN: 9780321794710

7th Edition

Authors: Robert V., Joseph W. McKean, Allen T. Craig

See More Books

Question Posted: Oct 13, 2022 02:22 AM

See More Questions

Let X have the gamma distribution with parameters > 2 and > 0. a. Prove that the mean of 1/X is /( 1). b. Prove that the variance of 1/X is 2/[( 1)2 ( 2)].
Let X have the gamma distribution with parameters n and 3, where n is a large integer. a. Explain why one can use the central limit theorem to approximate the distribution of X by a normal...
Show that the variance of a gamma distribution with parameters and is 2 .
C) Use the appropriate Maxwell relation and determine whether the specific heat capacity at constant pressure (Cp) is a function of pressure at onstant temperature for: i) An ideal gas ii) [6 marks]...
Classify each item in the following list of cash receipts and cash payments as operating, investing, or financing under IFRS. Cash Receipt or Payment ClassificationIFRS Cash payments to suppliers and...
FedEx Corporation had the following revenue and expense account balances (in millions) for a recent year ending May 31: Depreciation Expense ................................ $3,095 Purchased...
On June 14, 1988, Thomas John Heck Jr. executed a note promising to pay Paul D. Heck $$51,000$ at 7 percent interest compounded annually. The note contains the following payment terms: Perpetual 90...
Stagg Construction Co. is leasing equipment from Cloud Inc. The lease calls for payments of $50,000 a year plus $3,000 a year executory costs for five years. The first payment is due on January 1,...
Write the following expression in expanded form. (x+5)4 In (x-1)x+2
Lu Corp. erected and placed into service an offshore oil platform on January 1, 2020 at a cost of $10 million. Lu is legally required to dismantle and remove the platform at the end of its nine-year...
Toss two nickels and three dimes at random. Make appropriate assumptions and compute the probability that there are more heads showing on the nickels than on the dimes.
Compute the measures of skewness and kurtosis of the Poisson distribution with mean .
Alka-Seltzer contains sodium bicarbonate (NaHCO3) and citric acid (H3C6H5O7). When a tablet is dissolved in water, the following reaction produces sodium citrate, water, and carbon dioxide (gas):...
Write the code for the assignment below and upload the zipped src folder to the learning hub (learn.bcit.ca Activities Assignments Assignment 2) before the dropbox due date. Include your full name at...
(3 points) For p(x)= =-512+ 2304x 4608x2 +5376x3 4032x+2016x5-672x6 +144x7 - 18x8 + 12 Write a MATLAB program to evaluate p(3.24) by Horner's algorithm (nested multiplication). Enter the result to at...
A solid sphere has a mass of 2kg and radius 10cm starts from rest and rolls down a sloped surface at an angle of 37 from the horizontal without slipping. What is the translational speed of the of the...
$ 3 5 , 0 0 0 will be collected in January and the remaining amount will be collected in February. The monthly expense figures include $ 5 , 0 0 0 of depreciation. The expenses are paid in the month...
Norris has the following capital structure: Preferred stock, 6 % , $ 1 5 par, 2 0 , 0 0 0 shares issued and outstanding for the year Common stock, $ 1 par, 1 0 0 , 0 0 0 shares issued and outstanding...
Refer to Problem 5.37. If you purchased a 2009 Dodge, what is the probability that the new car will have a. Zero problems? b. Two or fewer problems? c. Compare your answers in (a) and (b) to those...
(a) What do data breach notification laws require? (b) Why has this caused companies to think more about security?
Suppose that two fair dice (one red and one green) are rolled. Define the events A: a 1 or a 2 shows on the red die B: a 3, 4, or 5 shows on the green die C: the dice total is 4, 11, or 12 Show that...
A roulette wheel has thirty-six numbers colored red or black according to the pattern indicated below: Define the events A: red number appears B: even number appears C: number is less than or equal...
How many probability equations need to be verified to establish the mutual independence of four events?
Looking ahead to the next decade, estimate likely standards of value creation. How would you advise a company like IBM or Cisco to configure and coordinate their value chain to thrive in this...
KNOWLEDGE CHECK egendary investor Warren Buffett said, "Gold gets dug out of he ground... Then we melt it down, dig another hole, bury it gain and pay people to stand around guarding it. It has no...
The primary purpose of internal and external audits on real estate trust accounts is to: Question 6Answer a. Ensure the funds are invested with high returns. b. Check the efficiency of the real...

Let X have a gamma distribution with parameters and . Show that P(X 2)

Question:

Step by Step Answer:

Solution The mgf for X is Mt 1 t for t 1 Assume that e...View the full answer

Introduction To Mathematical Statistics

Students also viewed these Business questions