Homework Help is Here – Start Your Trial Now!
Math
Statistics
Given X = {0, 1} with X = 1 indicating disease. Given their status, a diagnostic test returns a classification of Y = {0, 1} with Y= 1 indicating a positive result: X~ Ber(p) Y | X~ Ber(px) Recall that the pmf of a generic Ber(π) random variable, W, is fw (w) = pw(1 − p)¹-w 0 < π≤ 1 for w = {0, 1} and fw (w) = 0 elsewhere. 1. Find the marginal expectation E[Y] in terms of p, p₁, and po. 2. Find the Cov(Y, X) in terms of p, p₁, and po. 3. Find an expression for P(X = 1 | Y = y) only in terms of y = p², and p. 4. Prove that the conditional variance of X is V[X | Y = y] = P(X = 1 | Y = y)(1 − P(X = 1 | Y = y))

Given X = {0, 1} with X = 1 indicating disease. Given their status, a diagnostic test returns a classification of Y = {0, 1} with Y= 1 indicating a positive result: X~ Ber(p) Y | X~ Ber(px) Recall that the pmf of a generic Ber(π) random variable, W, is fw (w) = pw(1 − p)¹-w 0 < π≤ 1 for w = {0, 1} and fw (w) = 0 elsewhere. 1. Find the marginal expectation E[Y] in terms of p, p₁, and po. 2. Find the Cov(Y, X) in terms of p, p₁, and po. 3. Find an expression for P(X = 1 | Y = y) only in terms of y = p², and p. 4. Prove that the conditional variance of X is V[X | Y = y] = P(X = 1 | Y = y)(1 − P(X = 1 | Y = y))

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
See similar textbooks
icon
Related questions
Question

Kindly answer question 3 and 4

Given X = {0, 1} with X = 1 indicating disease. Given their status, a diagnostic test returns a classification of Y = {0, 1} with Y= 1 indicating a positive result: X ~ Ber(p) Y | X Ber(px) Recall that the pmf of a generic Ber(π) random variable, W, is fw (w) = pw(1 − p)¹-w - 0 = π = 1 for w = {0, 1} and fw (w) = 0 elsewhere. 1. Find the marginal expectation E[Y] in terms of p, p₁, and po. 2. Find the Cov(Y, X) in terms of p, p₁, and po. 3. Find an expression for P(X = 1 | Y = y) only in terms of y = P², and p. 4. Prove that the conditional variance of X is V[X | Y = y] = P(X = 1 | Y = y)(1 − P(X = 1 | Y = y))
Transcribed Image Text:Given X = {0, 1} with X = 1 indicating disease. Given their status, a diagnostic test returns a classification of Y = {0, 1} with Y= 1 indicating a positive result: X ~ Ber(p) Y | X Ber(px) Recall that the pmf of a generic Ber(π) random variable, W, is fw (w) = pw(1 − p)¹-w - 0 = π = 1 for w = {0, 1} and fw (w) = 0 elsewhere. 1. Find the marginal expectation E[Y] in terms of p, p₁, and po. 2. Find the Cov(Y, X) in terms of p, p₁, and po. 3. Find an expression for P(X = 1 | Y = y) only in terms of y = P², and p. 4. Prove that the conditional variance of X is V[X | Y = y] = P(X = 1 | Y = y)(1 − P(X = 1 | Y = y))
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 5 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman
SEE MORE TEXTBOOKS