If X and Y have the joint probability distributionf(−1, 0) = 0, f(−1, 1) = 1 4 , f(0, 0) = 16 , f(0, 1) = 0, f(1, 0) = 112 , and f(1, 1) = 12 , show that (a) cov(X, Y) = 0;(b) the two random variables are not independent.

If X and Y have the joint probability distributionf(−1, 0) = 0, f(−1, 1) = 1 4 , f(0, 0) = 16 , f(0, 1) = 0, f(1, 0) = 112 , and f(1, 1) = 12 , show that (a) cov(X, Y) = 0;(b) the two random variables are not independent.

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter13: Probability And Calculus

Section13.CR: Chapter 13 Review

Problem 3CR

See similar textbooks

Related questions

Q: X is a discrete random variable and takes the values 0,1 and 2 with probabilities of 1/6, 1/3 and…

A: Moment generating function:

Q: 1- X and Y are independent random variables and have U(0,1) distribution. Let Z = min{X,Y}. Find…

A: Solution

Q: If X and Y are two independent random variables such that E[X]=2, variance of X = o}, E[Y]= 1, and…

Q: If two random variables, X and Y, are independent, then the joint characteristic function is equal…

Q: If X and Y are two random variables, then the covariance is Cxy = Ryy – XY

Q: : Discrete random variables X and Y have the joint PMF| c(r+ y)², x= -1,0, 1; y = -2,0, 2,…

A: Note: Hi there! Thank you for posting the question. As your question has more than 3 parts, we have…

Q: The random variables X and Y have joint pdf (x(1+3y²) fxy (x, y) = 0 < x < 2, 0< y < 1 4 0,…

A: Solution: The joint pdf of (X,Y) is given by fXY(x,y)=x(1+3y2)4 0<x<2, 0<y< 10…

Q: The random variables X₁, X2, and X3 are Stochastic Independent with respective means 9, 4, and 16…

A: Consider three random variables X1, X2, X3, where, X1 have mean µ1 and variance σ12, X2 have mean µ2…

Q: X is a continuous random variable taking values between 0 and 2. If F(1.5) = 0.70 and P(X<1) = 0.20,…

Q: If X and Y are two random variables, then the covariance of x+a,Y +b,where a and b are constant is…

Q: for r, y > 0, f(x, y) = (1+x)2.(1+xy)² > 0, otherwise. Show that X and X Y are independent,…

A: *answer:

Q: X³, 2Y²-3Y+4) Calculate the covariance by creating a common distribution table for the given…

Q: Find the steady state probability vector fe Av = v and the components of v sum to 0.6 0.1 0.4 0.9

Q: Let Y1 =;(X2 - X2), Y2 = X2 where X1 and X2 are stochastically independent random variable each…

Q: Two random variables X and Y have the joint pdf, fx, y(x, y) = Ae12x+y), = 0, X, y 2 0 elséwhere (1)…

Q: (X³ , 2Y²-3Y+4) Calculate the covariance by creating a common distribution table for the given…

A: Given : (X³ , 2 Y²-3 Y+4)

Q: Let us say that we have jointly distributed random variables X and Y with E(X) = 3, E(Y) = 5, Var…

Q: X and Y be two discrete random variables with a joint p en by X-0 X-2 Y=1 0.03 0.02

A: to find P(X>0 and Y≤3)

Q: Let X and Y be two random variable with E(X) = 1,Var(X) = 2, E(Y) = 2,Var(Y) = 2. Then Cov(X –…

A: GivenE(x)=1Var(x)=2E(y)=2Var(y)=2

Q: Let X and Y are two independent random variables with probabilities P(X) = {0.25,0.45,0.3} and P(Y)…

Q: Let the joint pdf of random variables X, Y be fx,y (r, y) = axye-2-3y, for all æ > 0, y 2 0. Find a,…

A: We have given that a joint pdf of variables X and Y.

Q: The random variables X1,..., Xn are independent and identically distributed with probability…

A: Given information: The probability density function of the random variables X and Y is given.

Q: Consider two assets (X and Y) with µx = 10%, µy = %3D 10%, o x=.16, o,=.25, and Cov(X,Y) = -.125.…

A: Solution: Note: Hello! As you have posted more than 3 sub parts, we are answering the first 3…

Q: If the random variables X and Y are orthogonal, then their correlation is zero. Rxy =0

Q: Let X and Y be two (continuous or discrete) random variables with E(X)=D2, E(Y)3D5, Var(X)=9,…

A: Given: E(X) = 2 E(Y) = 5 Var(X) = 9 Var(Y) = 16 Cov(X,Y) = 5 Formula Used: Var(X-Y) = V(X) - V(Y) -…

Q: Suppose you have joint random variables X and Y. a) If a problem does not state anything about…

A: X and Y are 2 R.V. and if the dist. of X is not influenced by Y values then 2 R.V. are independent.

Q: Let X and Y be jointly Gaussian random variables with PDF exp { (12 + 4y² – 2x + 1) } fx,y(x, y) for…

Q: X1 and X2 are independent random variables each distributed as N (0, 1). Show that the MGF of (X,-…

Q: f X1 and X2 are independent exponential random variables with respective parameters λ1 and λ2, find…

A: Given: X1, X2 are two independent exponential random variables with respective parameters λ1 and…

Q: The joint PMF of two random variables X and Y is given by (k(2x + y), ((2x) Pxy (x, y) 0, Where k is…

Q: If Y is an exponential random variable with parameter , then μ = E(Y) = 8 and o² = V(Y) = 8². The…

A: We have given that Y is an exponential random variable with parameters beta then mean = E(Y) = β…

Q: PMF of random variable X is defined as 0.2 X = -2 0.1 X = -1 0.1 X = 0 Px (x) = {0 X = 1 ve X = 2…

Q: Let X1, X2, X3 be random variables each having a mean u and variance o'. Further, Cov(X1 X2) 2,…

A: The mean of a constant is equal to the value of the constant and the mean of sum of random variables…

Q: Let Z be a discrete random variable withE(Z)=0. Does it necessarily follow that E(Z3)=0? If yes,…

A: Solution

Q: Find the covariance and the correlation coefficient between X and Y, if X and Y are jointly discrete…

A: For the given data Find the covariance and correlation between x and y

Q: X and Y are independent random variables uniformly distributed over (0, 1). Compute the probability…

Q: The joint p.d.f of a two-dimensional random variables (x, y) is given by f(x,y) = kxe , 0 0 = 0 ,…

A: To find k, we need to apply total probability =1.

Q: If X(n,p) is a binomial random variable with parameters n and p, then why is it that X(n+1,p)…

A: Given that X(n, p) is a binomial random variable with parameters n and p.We will prove the given…

Q: X is a random variable with the probability distribution f(X)= :X= 0,1,2. Then the mean of X is…

A: Given function is: f(X)=X2;X=0,1,2

Q: If X1 and X2 are independent random variables havingexponential densities with the parameters θ1 and…

Q: If a random variable X follows the process below, dX; = -kX,dt + odWt, W is a standard Brownian…

A: A random variable is a numerical description of the outcome of a statistical experiment. A random…

Q: The joint pdf of two variables X and Y is fxy(x, y) = 18 X and Y are independent random variables.…

Q: If the joint pdf of a two dimensional random variable (X,Y) is given by xy ху 0 <x<1&0< y < 2 + f…

A: Given information: Let X and Y be two random variables there joint pdf is given by; f(x,y)=x2+xy3…

Q: Show that if X', Y' are the deviations of the random variables X and Y from their respective means,…

A: In our daily life, we all may come across some situations that one variable that is related to other…

Q: If the joint pdf of the bivariate random variables X and Y is given by f(x,y) = 6 e-2x - 3Vx > 0,…

Q: random variables with E(X) =2, E(Y)=3 ,V(X)=4,V(Y)=16. Find a)E(5X-Y) b)V(5X-Y) c)COV(3X+Y,Y)…

Question

If X and Y have the joint probability distribution
f(−1, 0) = 0, f(−1, 1) = 1

4 , f(0, 0) = 1
6 , f(0, 1) =

0, f(1, 0) = 1
12 , and f(1, 1) = 1
2 , show that

(a) cov(X, Y) = 0;
(b) the two random variables are not independent.

Video Video

Expert Solution

This question has been solved!

Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.

SEE SOLUTION Check out a sample Q&A here

Step 1

VIEW

Step 2

VIEW

Step 3

VIEW

Step by step

Solved in 3 steps with 4 images

SEE SOLUTION Check out a sample Q&A here

Knowledge Booster

$Multivariate Distributions and Functions of Random Variables$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, statistics and related others by exploring similar questions and additional content below.