Question: Let X have a beta distribution with parameters α and β. (a) Show that the mean and variance of X are, respectively (b) Show that

Let X have a beta distribution with parameters α and β.
(a) Show that the mean and variance of X are, respectively
Let X have a beta distribution with parameters α and

(b) Show that when α > 1 and β > 1, the mode is at x = (α ˆ’ 1)/(α + β ˆ’ 2).

and --

Step by Step Solution

★★★★★

3.42 Rating (171 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

a EX EX 2 Thus b Set fx equ... 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

Document Format (1 attachment)

Word file Icon

579-M-S-D-D (704).docx

120 KBs Word File

Students Have Also Explored These Related Statistics Questions!

Q:

A random variable X is said to have a beta distribution with parameters a and if and only if the density function of X is (a) Show that (b) Show that a. > 0; 0

Q:

Let X1 and X2 have independent gamma distributions with parameters α, θ and β, θ, respectively. Let W = X1/(X1 + X2). Use a method similar to that...

Q:

Let X be a random variable with an Fp,q distribution. (a) Derive the pdf of X. (b) Derive the mean and variance of X. (c) Show that 1/X has an Fp,q distribution. (d) Show that (p/q)X/[ 1 + (p/q)X\...

Q:

Let X have the binomial distribution with parameters n and p. Let Y have the binomial distribution with parameters n and p/k with k > 1. Let Z = kY. a. Show that X and Z have the same mean. b. Find...

Q:

Read through the attachments below and answer the questions accordingly. Currently there is a debate about cigarette advertising. Some anti-smoking advocates would like to ban cigarette advertising....

Q:

Read through the following questions and answer them approximately. Question 5.11 A random variable X has a Gamma distribution with parameters o and 1. (i) Show that the moment generating function of...

Q:

Answer all questions precisely. Please explain your answers fully. Question one. a) Define the term cross price elasticity of demand and explain its value for substitutes andcomplementary...

Q:

9. (Bayes rate) Suppose a drug test is 99% sensitive and 99% specic. That is, the test will produce 99% true positive results for drug users and 99% true negative results for nonidrug users: P(Test =...

Q:

7.31 Order statistics. Suppose X1,...,X100 are independent and uniformly distributed on (0,1). (a) Find the probability the 25th smallest variable is less than 0.20. (b) Find E[X(95)] and V [X(95)]....

Q:

Gaussian distribution 4. The figure has two spherical shells and three different possible gaussian surfaces. If both shells have a charge of 5nC what is the electric field at the innermost gaussian...

Q:

Below we give two contingency tables of data from reports submitted by airlines to the U.S. Department of Transportation. The data concern the numbers of on-time and delayed flights for Alaska...

Q:

DATABEAM is a new company that develops computer games for the 'corporate market' based on politics and advancement in a large Fortune 500 company. Their company has the following positions:...

Q:

On which accounting system ( parent , subsidiary, other ) are the consolidation elimination entries posted? Why? There are five end - of - year journat entries when consolidating financial statements...

Q:

To what extent are sales promotions effective in the short and the long term?

Q:

Harrington Health Food stocks 5 loaves of Neutro-Bread. The probability distribution for the sales of Neutro-Bread is listed in the following table. How many loaves will Harrington sell on average?...

Q:

What are the expected value and variance of the following probability distribution? RANDOM VARIABLE X PROBABILITY 1 ................0.05 2 ................0.05 3 ................0.10 4...

Q:

There are 10 questions on a true-false test. A student feels unprepared for this test and randomly guesses the answer for each of these. (a) What is the probability that the student gets exactly 7...

Q:

The Zip file: https://www150.statcan.gc.ca1/tbl/csv/32100008-eng.zip A. (1 point) Obtain the Trade Data of monthly export of grains from Statistics Canada's Open Government. See also...

Q:

12.2 One sample has n = 15 with SS = 1570, and a second sample has n = 15 with SS = 1650. a. Find the pooled variance for the two samples. b. Compute the estimated standard error for the sample mean...

Q:

stock has had the following year-end prices and dividends: Year Price ($) Dividend ($) 1 93.27 - 2 91.08 1.22 3 95.38 1.29 4 95.28 1.34 5 96.87 1.53 6 97.72 1.65 What is the geometric average return...