Explanation Calculation: The function of gamma is, Γ ( r ) = ∫ 0 ∞ x r − 1 e − x d x By using integration by parts, By ILATE rule, u = x r − 1 and d v d x = e − x . The general formula is, ∫ a b u ( d v d x ) d x = ( u v ) a b − ∫ a b v ( d u d x ) d x By applyinf this formula, Γ ( r ) = ∫ 0 ∞ x r − 1 e − x d x = ( x r − 1 ( − e − x ) ) 0 ∞ − ∫ 0 ∞ ( − e − x ) ( d d x x r − 1 ) d x = ( x r − 1 ( − e − x ) ) 0 ∞ − ∫ 0 ∞ ( − e − x ) ( ( r − 1 ) x r − 2

Applied Statistics and Probability for Engineers

6th Edition

ISBN: 9781118539712

Author: Douglas C. Montgomery

Publisher: WILEY

See similar textbooks

Concept explainers

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differentia…

Videos

Question

Chapter 4.9, Problem 146E

To determine

Show that the Γ(r)=(r−1)Γ(r−1)

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 4.9, Problem 145E

Chapter 4.9, Problem 147E

Students have asked these similar questions

Morningstar tracks the total return for a large number of mutual funds. The following table shows the total return and the number of funds for four categories of mutual funds. Click on the datafile logo to reference the data. DATA file Type of Fund Domestic Equity Number of Funds Total Return (%) 9191 4.65 International Equity 2621 18.15 Hybrid 1419 2900 11.36 6.75 Specialty Stock a. Using the number of funds as weights, compute the weighted average total return for these mutual funds. (to 2 decimals) % b. Is there any difficulty associated with using the "number of funds" as the weights in computing the weighted average total return in part (a)? Discuss. What else might be used for weights? The input in the box below will not be graded, but may be reviewed and considered by your instructor. c. Suppose you invested $10,000 in this group of mutual funds and diversified the investment by placing $2000 in Domestic Equity funds, $4000 in International Equity funds, $3000 in Specialty Stock…

The days to maturity for a sample of five money market funds are shown here. The dollar amounts invested in the funds are provided. Days to Maturity 20 Dollar Value ($ millions) 20 12 30 7 10 5 6 15 10 Use the weighted mean to determine the mean number of days to maturity for dollars invested in these five money market funds (to 1 decimal). days

c. What are the first and third quartiles? First Quartiles (to 1 decimals) Third Quartiles (to 4 decimals) × ☑ Which companies spend the most money on advertising? Business Insider maintains a list of the top-spending companies. In 2014, Procter & Gamble spent more than any other company, a whopping $5 billion. In second place was Comcast, which spent $3.08 billion (Business Insider website, December 2014). The top 12 companies and the amount each spent on advertising in billions of dollars are as follows. Click on the datafile logo to reference the data. DATA file Company Procter & Gamble Comcast Advertising ($billions) $5.00 3.08 2.91 Company American Express General Motors Advertising ($billions) $2.19 2.15 ETET AT&T Ford Verizon L'Oreal 2.56 2.44 2.34 Toyota Fiat Chrysler Walt Disney Company J.P Morgan a. What is the mean amount spent on advertising? (to 2 decimals) 2.55 b. What is the median amount spent on advertising? (to 3 decimals) 2.09 1.97 1.96 1.88

Chapter 4 Solutions

Applied Statistics and Probability for Engineers

Ch. 4.2 - 4-1. Suppose that f(x) = e−x for 0 < x. Determine...Ch. 4.2 - 4-2. Suppose that f (x) = 3(8x – x2)/256 for 0< x...Ch. 4.2 - 4-3. Suppose that f (x) = 0.5 cos x for −π/2 < x <...Ch. 4.2 - Prob. 4E Ch. 4.2 - 4-5. Go Tutorial Suppose that for 3 < x < 5....Ch. 4.2 - Prob. 6E Ch. 4.2 - 4-7. Suppose that f(x) = 1 .5x2 for −1 < x < 1....Ch. 4.2 - 4-8. The probability density function of the time...Ch. 4.2 - 4-9. The probability density function of the net...Ch. 4.2 - Prob. 10E

Knowledge Booster

$Statistics$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.

Show that the Γ ( r ) = ( r − 1 ) Γ ( r − 1 )

Concept explainers

Videos

Show that the Γ(r)=(r−1)Γ(r−1)

Want to see the full answer?

Chapter 4 Solutions