Question: The Gamma probability density function is Where a and ( are positive constants. (Both the gamma and the Weibull distributions are used to model lifetimes

The Gamma probability density function is

Where a and ( are positive constants. (Both the gamma and the Weibull distributions are used to model lifetimes of people, animals, and equipment.)
(a) Find the value of C, depending on both a and (, that makes f(x) a probability density function.
(b) For the value of C found in part (a), find the value of the mean (.
(c) For the value of C found in part (a), find the variance (2?

if x s 0

Step by Step Solution

★★★★★

3.40 Rating (163 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock

a Let y b x so x y b and dx 1 b dy C b a a 1 ... View full answer

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)

955-M-C-D-E (2435).docx

120 KBs Word File

Students Have Also Explored These Related Calculus Questions!

What is a probability density function? What properties does such a function have?

Let f (x,y) be the probability density function of the continuous random variable (X, Y). If U = XY, show that the probability density function of U is given by dv fu(u)

Use a computer package to (ind both the probability density function and cumulative distribution function at x = 3 and the median of gamma distributions with the following parameter values: (a) k =...

Exercises Chapter 2 2.1 Marginal and conditional probability: The social mobility data from Section 2.5 gives a joint probability distribution on (Y1 , Y2 )= (father's occupation, son's occupation)....

1. A player throws a fair die and simultaneously flips a fair coin. If the coin lands heads, then she wins twice, and if tails, then one-half of the value that appears on the die. Determine her...

Write 2 paragraphs about Macro risks and the term structure of interest rates article. No max word count, page count, or formatting requirements but has to be submit to my tutor's work as my own....

11/26/2016 Fall 2016 Homework 12Due Thursday 12/1, before 8 PM. Must submit before 8PM. My sites / 16F-STATS100A-1 / HOMEWORK / Fall 2016- Homework 12-Due Thursday 12/1, before 8 PM. Must submit...

Possible Multiple Choice Questions for the Exam. Focus on the topics discussed in class. Chapter 1 Multiple Choice Identify the choice that best completes the statement or answers the question. ____...

MATHEMATICS FOR MACHINE LEARNING Marc Peter Deisenroth A. Aldo Faisal Cheng Soon Ong Contents Foreword 1 Part I Mathematical Foundations 9 1 Introduction and Motivation 11 1.1 Finding Words for...

kindly solve the question CASE STUDY WHICH IS BETTER-DEBT OR EQUITY FINANCING? Background Information Pizza Hut Corporation has decided to enter the catering busi- Plan A is debt financing for 50% of...

The end result of most viral infections is death of the host cell. a. If this is the case, how can we account for such differences in the damage that viruses do? b. Describe the adaptation of viruses...

Foot length: 25.0 cm; 99% confidence. Use the paired data consisting of foot lengths (cm) and heights (cm) of the 40 people listed in Data Set 2 of Appendix B. Let x represent foot length and let y...

Consider the following autonomous first - order differential equation. dydx = ( y 5 ) 4 Find the critical points and phase portrait of the given differential equation.

Are you in an entrepreneurial university?

(a) Use a graph to guess the value of the limit (b) Use a graph of the sequence in part (a) to find the smallest values N of that correspond to ( = 0.1 and in Definition 2. lim n!

Prove Theorem 6. If |an| = 0 Then an = 0.

What annual interest rate do you need to find in order for a deposit of $500 to grow to $1,623 in 10 years if the bank compounds interest monthly? Select one: a. 11.36 percent b. 12.50 percent c....

Question 1 The real risk-free rate is expected to remain constant at 3% in the future, a 2% rate of inflation is expected for the next 2 years, after which inflation is expected to increase to 4%,...

Question 45 A same Mres syt. Mmbol detert or soint cumbination af these uted to identify the grotucts of one furm and differentiate them thon comornitive afierings it callicda too thes"nume pominaset...