(a) Prove or disprove the following statements. (i) If two random variables are independent, then the covariance be (ii) If cov (X, Y) =0, then X and Y are independent. (b) Let X and Y be two discrete random variables: P{X = x,} = P1. P{X = x2} = 1-p,: %3D and P{Y = y,} = P2; P{Y=y2} = 1-p2. Show that X and Y are independent if and only if the correlation coeffi

(a) Prove or disprove the following statements. (i) If two random variables are independent, then the covariance be (ii) If cov (X, Y) =0, then X and Y are independent. (b) Let X and Y be two discrete random variables: P{X = x,} = P1. P{X = x2} = 1-p,: %3D and P{Y = y,} = P2; P{Y=y2} = 1-p2. Show that X and Y are independent if and only if the correlation coeffi

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter10: Sequences, Series, And Probability

Section10.8: Probability

Problem 31E

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Concept explainers

Correlation

Correlation defines a relationship between two independent variables. It tells the degree to which variables move in relation to each other. When two sets of data are related to each other, there is a correlation between them.

Linear Correlation

A correlation is used to determine the relationships between numerical and categorical variables. In other words, it is an indicator of how things are connected to one another. The correlation analysis is the study of how variables are related.

Regression Analysis

Regression analysis is a statistical method in which it estimates the relationship between a dependent variable and one or more independent variable. In simple terms dependent variable is called as outcome variable and independent variable is called as predictors. Regression analysis is one of the methods to find the trends in data. The independent variable used in Regression analysis is named Predictor variable. It offers data of an associated dependent variable regarding a particular outcome.

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(a) Prove or disprove the following statements.
(i) If two random variables are independent, then the covariance between them is zero.
(ii) If cov (X, Y) =0, then X and Y are independent.
(b) Let X and Y be two discrete random variables:
P{X =x,} = P1.
P{X =x,} = 1-p,;
and
P{Y=y,} = P2,
P{Y= y2} = 1-P2-
Show that X and Y are independent if and only if the correlation coefficient between X and Y is zero.
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