A market researcher wants to determine whether a new model of a personal cormputer that had been advertised on a late-night talk show had achieved more brand-name recognition among people who watched the show regularly than armong people who did not. After conducting a survey, it was found that 12% of all people both watched the show regularly and could correctly identify the product. Also, 13% of all people regularly watched the show and 44% of all people could correctly identify the product. Define a pair of random variables as shown below. Complete parts (a) through (c). X=1 if regularly watch the show Y=1 if product correctly identified X=0 otherwise Y=0 otherwise a. Find the joint probability function of X and Y. X 1 Y 1 (Do not round.) b. Find the conditional probability function of Y, given X= 1. P(0| 1) = (Round to three decimal places needed.) P(1| 1) = (Round to three decimal places as needed.) c. Find and interpret the covariance between X and Y. Cov(X,Y) =(Do not round.) Interpret the covariance. O A. The covariance indicates that there is a negative association between watchers of a late-night talk show and brand-name recognition. O B. The covariance indicates that there is a positive association between watchers of a late-night talk show and brand-name recognition.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Transcribed Image Text:Amarket researcher wants to determine whether a new model of a personal cormputer that had been advertised on a late-night talk show had achieved more brand-name recognition among people who watched the show regularly than armong people who did not. After conducting a survey, it was found that 12% of all people both watched the show regularly and could correctly identify the product. Also, 13% of all people regularly watched the show and 44% of all people could correctly identify the product. Define a pair of random variables as shown below. Complete parts (a) through (c). X=1 if regularly watch the show Y=1 if product correcly identified X = Y =0 otherwise (%3D0 otherwise a. Find the joint probability function of X and Y. 1. Y (Do not round.) b. Find the conditional probability function of Y, given X= 1. P(0| 1) = (Round to three decimal places as necded.) P(1 | 1) = (Round to three decimal places as needed.) c. Find and interpret the covariance between X and Y. Cov(X, Y) = (Do not round.) Interpret the covariance. O A. The covariance indicates that there is a negative association between watchers of a late-night talk show and brand-name recognition. O B. The covariance indicates that there is a positive association between watchers of a late-night talk show and brand-name recognition.

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