
A First Course in Probability (10th Edition)
10th Edition
ISBN: 9780134753119
Author: Sheldon Ross
Publisher: PEARSON
expand_more
expand_more
format_list_bulleted
Question

Transcribed Image Text:67. Let X be a discrete random variable with pmf
(a) Find the pmf for Y = X².
(b) Find the pmf for U = X + 2.
f(x) = px(x) =
1/8,
1/4,
1/4,
1/4,
1/8,
0,
x = -2
x = -1
x = 0
x = 1
x = 2
otherwise
Expert Solution

This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by stepSolved in 4 steps

Knowledge Booster
Similar questions
- The probability mass function for a discrete random variable X is defined as ((1+0)-(x) 0; x = 0,1,2,3,..., η (x) = {(1+0) (2) *; fx(x) 0; e.w. where 0 > 0. Show that it is probability mass function. Find its mean and variance.arrow_forwardLet X and Y be two random variables with Var(X) = 6, Var(Y ) = 3, andthe correlation ρ(X, Y ) = −1/4. Find the value of Var(X − 2Y + 7).arrow_forwardE(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…arrow_forward
- Let X1, X2, and.X3 be independent and normally distributed random variables with E(X1) 4, E(X2) = 3, E(X3) = 2, Var(X1) = 1, Var(X2) = 5, Var(X3) = 2. Let Y = 2X1 + X2 – 3X3. Find 2. the distribution of Y.arrow_forwardCov(X,Y) 1) The correlation of two random variables X and Y, usually written as p(X,Y)= Var (X)Var (Y) where Cov(...) is the covariance and Var(.) is the variance of random variables. Let X be a uniform random variable on the interval [0; 1], and let Y = X2. Find the correlation between X and Y.arrow_forwardX is a continuous random variable and the pdf of X is k x> 1 f(x) xS 1 Determine the value of k for which f(x) is a legitimate pdf.arrow_forward
- please and thank you!!!arrow_forward(16) The moment-generating function of the geometric random variable X with parameter p is M(t) = 1-per. Use this to find the mean and variance of X.arrow_forwardN(0, o?) is For the simple linear model Y = a + BX + €, where the error variable e ~ independent of X, use the law of total variance to show that Var(Y) = 3² Var(X)+o².arrow_forward
arrow_back_ios
SEE MORE QUESTIONS
arrow_forward_ios
Recommended textbooks for you
- A First Course in Probability (10th Edition)ProbabilityISBN:9780134753119Author:Sheldon RossPublisher:PEARSON

A First Course in Probability (10th Edition)
Probability
ISBN:9780134753119
Author:Sheldon Ross
Publisher:PEARSON
