E(XY) – E(X)E(Y)1. The correlation of X and Y is defined as px,yif X and Y are independent, then px,y = 0.Quickly show thato(X)o(Y)2. Let X be a random variable with P(X = k) = | for k = -1,0, 1. Let Y = X².(a) What is the p.m.f. of Y?(b) Are X and Y independent?(c) Calculate E(XY) – E(X)E(Y).(d) True or false (for any random variables X and Y): X and Y are independent if and onlyif E(XY) – E(X)E(Y).3. An exam consists of twenty multiple choice questions. Each question has five different possibleanswers, only one of which is correct. A person randomly guesses on each question. What isthe variance of the number of questions that are correct?4. Suppose ten people get on an elevator. There are eight buttons representing floors on thiselevator. Each person presses a random button. The elevator will only stop at a floor if atleast one person pressed that floor's button. What is probability the elevator stops at exactlysix floors? What is the variance of the number of floors the elevator will stop at?5. A game costs $10 to play. In the game, you roll three fair six-sided dice. If you roll one six,you win $5. If you roll two sixes, you win $10. If you roll three sixes, you win $K. Whatvalue must K be so that the game is fair (the expected winnings are $0)?

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Answered: E(XY) – E(X)E(Y) σ(Χ)σ(Υ) 1. The…

E(XY) – E(X)E(Y) σ(Χ)σ(Υ) 1. The correlation of X and Y is defined as px,Y Quickly show that if X and Y are independent, then px,y = 0.

A First Course in Probability (10th Edition)

10th Edition

ISBN:9780134753119

Author:Sheldon Ross

Publisher:Sheldon Ross

Chapter1: Combinatorial Analysis

Section: Chapter Questions

Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...

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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.

Question

E(XY) – E(X)E(Y)
1. The correlation of X and Y is defined as px,y
if X and Y are independent, then px,y = 0.
Quickly show that
o(X)o(Y)
2. Let X be a random variable with P(X = k) = | for k = -1,0, 1. Let Y = X².
(a) What is the p.m.f. of Y?
(b) Are X and Y independent?
(c) Calculate E(XY) – E(X)E(Y).
(d) True or false (for any random variables X and Y): X and Y are independent if and only
if E(XY) – E(X)E(Y).
3. An exam consists of twenty multiple choice questions. Each question has five different possible
answers, only one of which is correct. A person randomly guesses on each question. What is
the variance of the number of questions that are correct?
4. Suppose ten people get on an elevator. There are eight buttons representing floors on this
elevator. Each person presses a random button. The elevator will only stop at a floor if at
least one person pressed that floor's button. What is probability the elevator stops at exactly
six floors? What is the variance of the number of floors the elevator will stop at?
5. A game costs $10 to play. In the game, you roll three fair six-sided dice. If you roll one six,
you win $5. If you roll two sixes, you win $10. If you roll three sixes, you win $K. What
value must K be so that the game is fair (the expected winnings are $0)?

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