For a multinomial (n, i ) distribution, show the correlation between p i and p j is i j (1 i )(1 j ) 1 2 What does this equal when i 1 j and k 0 for k i, j ...

This follows using Covp i p j n i j a ...

For a multinomial (n, { i }) distribution, show the correlation between p i and p j

Question:

For a multinomial (n, {π_i}) distribution, show the correlation between p_i and p_j is –[π_i π_j/(1 – π_i)(1 – π_j)]^1/2. What does this equal when π_i = 1 – π_j and π_k = 0 for k ≠ i, j?

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 12, 2018 08:30 AM

See More Questions

Determine the covariance and correlation for X1 and X2 in the joint distribution of the multinomial random variables X1, X2 and X3 in with p1 = p2 = p3 = 1/3 and n = 3. What can you conclude about...
This exercise requires ideas from Section 2.6. In a two-sample experiment, when each item in one sample is paired with an item in the other, the paired t test (Section 6.8) can be used to test...
Let (X1,..., Xn) have a multinomial distribution with m trials and cell probabilities p1,... ,pn (see Definition 4.6.2). Show that, for every i and j, Pi 1-Pi X, r binomial (m,p)
The national mean annual salary for a school administrator is $90,000 a year. A school official took a sample of 25 school administrators in the state of Ohio to learn about salaries in that state to...
In the system shown in Figure 8-26, suppose the block has a mass of 2.7 kg, the spring has a force constant of 480 N/m, and the coefficient of kinetic friction between the block and the floor is...
Mc Michaluk has a $50,000 personal (revolving) line of credit with the Canadian Imperial Bank of Commerce (CIBC). The loan is on a demand basis at a floating rate of prime plus 1.5%. On the fifteenth...
1. What are the characteristics of an operating segment under US GAAP or IFRS 8?
Let's investigate the possibility of heteroskedasticity in time-series data by looking at a model of the black market for U.S. dollars in Brazil that was studied by R. Dornbusch and C. Pechman. In...
Incredible Sounds is a wholesale business that sells musical instruments. Transactions involving sales and cash receipts for the firm during April 2021 follow. The firm sells its merchandise for cash...
Rice Corporation is negotiating a loan for expansion purposes and the bank requires financial statements. Before closing the accounting records for the year ended December 31, 2018, Rice's controller...
Consider the model for a 2 2 table. 11 = 2 , 12 = 21 = (1 ), 22 = (1 ) 2 , where is unknown (Problems 3.31 and 10.34). a. Find the matrix A in (14.14) for this model. b. Use A to obtain the...
a. Refer to Problem 14.6. If T n is Poisson, show T n has asymptotic variance 1/4. b. For a binomial sample with n trials and sample proportion p, show the asymptotic variance of sin -1 (p) is 1/4n....
Comment on the importance of value creation product strategies for transactional, consultative, and strategic alliance buyers.
Show that the scalar $K$, which, according to Eq. (5.366), is constructed from the extrinsic curvature as $K=g^{\mu v} K_{\mu u}$, is equal to the covariant divergence of the normal vector field,...
An aircraft is in flight, and its $\mathrm{TAS}=220 \mathrm{~m} / \mathrm{s}$. The ambient temperature is $T=253 \mathrm{~K}$. What is the stagnation temperature on its leading edge?
A diver's watch resists an absolute pressure of 5.5 bar. At an ocean having density of $1025 \mathrm{~kg} / \mathrm{m}^{3}$ and exposing an atmospheric pressure of $1 \mathrm{bar}$, what depth...
Estimate TAS if an aircraft is at ALT $=9500 \mathrm{~m}$ and its Mach number $M$ is 0.5 .
The Mach number of an aircraft is $M=0.9$, and the local temperature is $T=-10^{\circ} \mathrm{C}$. What is its airspeed?
In Exercises use integration by parts to find the indefinite integral. S e2x sin 3x dx
Determine the reactions in supports A and D and connections B and C. Sketch its shear and moment diagram and determine the magnitude ankoration of the maximum shear and moment for every member. 18 3...
An exam consists of 50 multiplechoice questions. Based on how much you studied, for any given question you think you have a probability of p = 0.70 of getting the correct answer. Consider the...
According to a Boston Globe story, only about 1 in 6 Americans have blue eyes, whereas in 1900 about half had blue eyes. (Source: Data from The Boston Globe, October 17, 2006.) a. For a random sample...
According to the Alzheimers Association1, as of 2011 Alzheimers disease affects 1 in 8 Americans over the age of 65. A study is planned of health problems faced by the elderly. For a random sample of...
Duncan Inc. issued 500, $1,200, 8%, 25 year bonds on January 1, 2020, at 102. Interest is payable on January 1. Duncan uses straight-line amortization for bond discounts or premiums. INSTRUCTIONS:...
WISE-HOLLAND CORPORATION On June 15, 2013, Marianne Wise and Dory Holland came to your office for an initial meeting. The primary purpose of the meeting was to discuss Wise-Holland Corporation's tax...
Stock in ABC has a beta of 0.9. The market risk premium is 8%, and T-bills are currently yielding 5%. The company's most recent dividend is $1.60 per share, and dividends are expected to grow at a 6%...

For a multinomial (n, { i }) distribution, show the correlation between p i and p j

Question:

Step by Step Answer:

This follows using Covp i p j n i j a...View the full answer

Categorical Data Analysis

Students also viewed these Mathematics questions