Using E(Y) = E[E(Y | X)] and var(Y) = E[var(Y | X)] + var[E(Y | X)], derive

Question:

Using E(Y) = E[E(Y | X)] and var(Y) = E[var(Y | X)] + var[E(Y | X)], derive the mean and variance of the

(a) Beta-binomial distribution,

(b) Negative binomial distribution.

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

Step by Step Answer:

Related Book For book-img-for-question

Categorical Data Analysis

ISBN: 9780471360933

2nd Edition

Authors: Alan Agresti

See More Books

Question Posted: Nov 17, 2018 10:34 AM

See More Questions

Random variable X and Y have joint PDF Answer the following questions (a) What are E[X] and Var [X]? (b) What are E[Y] and Var [Y]? (c) What is Cov[X + Y]? (d) What is E[X + Y]? (e) What is Var[X +...
X and Z are independent random variables with E[X] = E[Z] = 0 and variance Var [X] = 1 and Var [Z] = 16. Let Y = X + Z. Find the correlation coefficient p of x and Y, Are X and Y independent?
We can take the approach to selecting a prior distribution for a population proportion p proposed in Exercise 11 one step further. Recall that the variance of a beta random variable, Y, is given by...
Problem 5: Closing entries. (10 points) Given the following accounts, prepare the closing entries in the order and method taught using Income Summary. Number each entry 1, 2, .... Accounts payable $...
What do we mean when we say that outer space is not really empty?
An 80.0-kg skydiver jumps out of a balloon at an altitude of 1 000 m and opens the parachute at an altitude of 200 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N...
Explain why the quantity of transactions balances held by consumers and firms domestically would rise as the domestic money supply was increased by the central bank.
A local bank makes automobile loans. It charges 4% per year in the following manner: if$3600 is borrowed to be repaid over a 3-year period, the bank interest charge is $3600 x 0.04 x 3 years = $432....
The diagrams are showing stages of mitosis in a(n) cell. The stage shown in diagram A comes. shown in diagram B. Diagram A is showing spindle microtubules. animal; after; aiding in moving daughter...
Following are the 2015 balance sheet and income statement for the Woods Company. a. The firm operated at full capacity in 2015. During 2016, it expects sales to increase by 20 percent and dividends...
An alternative negative binomial parameterization results from the gamma density formula, for which E(Î») = µ, var(Î») = µ/k. Show that this gamma mixture of...
When y 1 ,..., y N are independent from the negative binomial distribution (13.13) with k fixed, show that ? = y. k ( + k) (k)( + 1) etk k k p(y;k, ) 1 u + k %3D 0,1, 2, ....
A physicist scatters rays from a substance and sees evidence of a nucleus 7.5 x 10 -13 min radius. (a) Find the atomic mass of such a nucleus. (b) What is unreasonable about this result? (c) What is...
What do you think of the gainsharing plan that Harrah's has implemented? How does an employee make more money? How much more money can they make? Is the gainsharing plan motivating employees to...
How do power dynamics within an organization affect employee empowerment and autonomy, and what are the best practices for creating a balanced power structure ?
In thinking about management and incentive structures: What recommendations do you have for the Responsible Innovation team as they seek to better embed responsible innovation within employees'...
How do multinational companies adapt their corporate governance procedures and decisions to accommodate the different national and regional regulatory requirements and business ethics? Requirement: I...
How do "complexity theory" and the concept of "emergent properties" inform our understanding of organizational dynamics, particularly in the context of nonlinear interactions and unpredictable...
The most common injury that occurs among mountain climbers is trauma to the lower extremity (leg). Consequently, rescuers must be proficient in immobilizing and splinting fractures. In High Altitude...
For the following exercises, find the area of the triangle. Round to the nearest hundredth. 22 50 36
Refer to Example 10 on whether arthroscopic surgery is better than placebo. The following table shows the pain scores one year after surgery. Using software (such as MINITAB) that can conduct...
In the study of binge drinking mentioned in Exercise 10.3, the percent who said they had engaged in unplanned sexual activities because of drinking alcohol was 30.7% in 1999 and 23.0% in 2009. Is...
Refer to the previous exercise. Compare the placebo to the debridement group using a significance test. State the assumptions, and explain how to interpret the P-value. Knee Pain Score Group Placebo...
Only need help on 4B and 5. Exercise 9-21 Breakeven Planning; Profit Planning (LO 9-2, 9-3] Connelly Inc., a manufacturer of quality electric ice cream makers, has experienced a steady growth in...
A project with an initial cost of $32,000 is expected to provide cash flows of $12,900, $13,100, $16,200, and $10,700 over the next four years, respectively. If the required return is 8.1 percent,...
A company that is expecting to receive EUR 500,000 in 60 days is considering entering into an FX futures contract to lock an exchange rate to USD for the transaction. The FX rate on the contract is...

Using E(Y) = E[E(Y | X)] and var(Y) = E[var(Y | X)] + var[E(Y | X)], derive

Question:

Step by Step Answer:

a For the beta binomial Var Y En1 Va...View the full answer

Categorical Data Analysis

Students also viewed these Mathematics questions