Suppose the two-dimensional random variable (X, Y ) is uniformly distributed over the triangle of the figure.
Suppose the two-dimensional random variable (X, Y ) is uniformly distributed over the triangle of the figure.
a) What is f.d.p.c. of (X,Y). Calculate P(0 < X ≤ 1, Y > 1). Make a graphic sketch of the region
that you used to calculate the probability.
b) Determine the marginal distributions. (X, Y ) are independent?
c) Find E[X] ,V AR[X], E[Y ] e V AR[Y ];
d) Determine the conditional distributions. Use the conditionals to answer : (X, Y ) are
independent?
e) Calculate E[XY ], γ = Cov(X, Y ) and e ρ = Color(X, Y ). Use the correlation coefficient to
justify the independence between X and Y.
Homework Answers
Request Answer!
We need at least 10 more requests to produce the answer.
0 / 10 have requested this problem solution
The more requests, the faster the answer.
Add Answer to:
Suppose the two-dimensional random variable (X, Y ) is uniformly distributed over the triangle of the figure.
Let X and Y be continuous random variables with joint distribution function F(x, y), and let...
Let X and Y be continuous random variables with joint distribution function F(x, y), and let g(X, Y ) and h(X, Y ) be functions of X and Y . Prove the following: (a) E[cg(X, Y )] = cE[g(X, Y )]. (b) E[g(X, Y ) + h(X, Y )] = E[g(X, Y )] + E[h(X, Y )]. (c) V ar(a + X) = V ar(X). (d) V ar(aX) = a 2V ar(X). (e) V ar(aX + bY ) = a...
Exercise about two-dimensional random variables, independence and covariation: Suppose, two-dimensional random variable...
Exercise about two-dimensional random variables, independence
and covariation:
Suppose, two-dimensional random variable (X, Y) has probability density function as follows: 0y1 + f(x, y) 2xy) ,0 <x<1, otherwise 0 Find c Find marginal probability density functions of X and Y-find f(x) and f(y) and find if X and Y are independent; Find joint (X, Y) distribution function; Find covariation of X and Y find Cov(X, Y) and correlation p(X, Y). What can be concluded?
Suppose, two-dimensional random variable (X, Y)...
(3) A pair of random variables (X, Y) is distributed uniformly on the triangle with vertices...
(3) A pair of random variables (X, Y) is distributed uniformly on the triangle with vertices (0,0), (2,0) and (0. Find EX, EY, Cov(X,Y), E(max{X,Y)), P(X> Y), P(X 2 Y)
for 1 Sx soo and 2. Suppose that X and Y are continuous and jointly distributed...
for 1 Sx soo and 2. Suppose that X and Y are continuous and jointly distributed by the function f(x,y) = 1 Sy S. PAY ATTENTION TO THE SUPPORT REGION. a. Find the marginals for X and Y. b. Find the conditional probability density functions g(xly) and hylx). C. Determine whether or not X and Y are independent based on your results above. d. Calculate P(X+Y<5 Y = 3). e. Find E[X] f. Find E[Y] 8. Find E[XY] h. Find...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distributio...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer.
(20 points) Consider the following joint distribution of X and...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Sho...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Let Θ be a continuous random variable...
Suppose that X is uniformly distributed between 0 and 1. Given X = x, Y is...
Suppose that X is uniformly distributed between 0 and 1. Given X = x, Y is uniformly distributed between 0 and x2. (a) Determine E(Y |X = x) and then Var(Y |X = x). Is E(Y |X = x) a linear function of x? (b) Find f(x, y) using fX(x) and fY |X(y|x). (c) Find fY (y). (d) Find the conditional density of X given Y = y. (e) Find the correlation coefficient between X and Y .
Suppose (X, Y ) has bivariate normal distribution, E(X) = E(Y ) = 0,V ar(X) =...
Suppose (X, Y ) has bivariate
normal distribution, E(X) = E(Y ) = 0,V ar(X) = σX2 , V ar(Y ) =
σY2 and Correl(X, Y ) = ρ. Calculate the conditional expectation
E(X2|Y ).
I. Suppose (X,Y) has bivariate normal distribution, E(X) = E(Y) 0, Var(X)-σ , Var(Y) σ and Correl (X,Y)-p. Calculate the conditional expectation ECKY expectation E(X2Y)
1. Suppose you have two random variables, X and Y with joint distribution given by the...
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Exercise about two-dimensional random variables, independence
and covariation:
Suppose, two-dimensional random variable (X, Y) has probability density function as follows: 0y1 + f(x, y) 2xy) ,0 <x<1, otherwise 0 Find c Find marginal probability density functions of X and Y-find f(x) and f(y) and find if X and Y are independent; Find joint (X, Y) distribution function; Find covariation of X and Y find Cov(X, Y) and correlation p(X, Y). What can be concluded?
Suppose, two-dimensional random variable (X, Y)...
(3) A pair of random variables (X, Y) is distributed uniformly on the triangle with vertices (0,0), (2,0) and (0. Find EX, EY, Cov(X,Y), E(max{X,Y)), P(X> Y), P(X 2 Y)
for 1 Sx soo and 2. Suppose that X and Y are continuous and jointly distributed by the function f(x,y) = 1 Sy S. PAY ATTENTION TO THE SUPPORT REGION. a. Find the marginals for X and Y. b. Find the conditional probability density functions g(xly) and hylx). C. Determine whether or not X and Y are independent based on your results above. d. Calculate P(X+Y<5 Y = 3). e. Find E[X] f. Find E[Y] 8. Find E[XY] h. Find...
(20 points) Consider the following joint distribution of X and Y ㄨㄧㄚ 0 0.1 0.2 1 0.3 0.4 (a) Find the marginal distributions of X and Y. (i.e., Px(x) and Py()) (b) Find the conditional distribution of X given Y-0. (i.e., Pxjy (xY-0)) (c) Compute EXIY-01 and Var(X)Y = 0). (d) Find the covariance between X and Y. (i.e., Cov(X, Y)) (e) Are X and Y independent? Justify your answer.
(20 points) Consider the following joint distribution of X and...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Let Θ be a continuous random variable...
Suppose (X, Y ) has bivariate
normal distribution, E(X) = E(Y ) = 0,V ar(X) = σX2 , V ar(Y ) =
σY2 and Correl(X, Y ) = ρ. Calculate the conditional expectation
E(X2|Y ).
I. Suppose (X,Y) has bivariate normal distribution, E(X) = E(Y) 0, Var(X)-σ , Var(Y) σ and Correl (X,Y)-p. Calculate the conditional expectation ECKY expectation E(X2Y)
1. Suppose you have two random variables, X and Y with joint distribution given by the following tables So, for example, the probability that Y o,x - 0 is 4, and the probability that Y (a) Find the marginal distributions (pmfs) of X and Y, denoted f(x),J(Y). (b) Find the conditional distribution (pmf) of Y give X, denoted f(YX). (c) Find the expected values of X and Y, EX), E(Y). (d) Find the variances of X and Y, Var(X),Var(Y). (e)...
Let Θ be a continuous random variable uniformly distributed on [0,2 Let X = cose and Y sin e. Show that, for this X and Y, X and Y are uncorrelated but not independent. (Hint: As part of the solution, you will need to find E[X], E[Y] and E|XY]. This should be pretty easy; if you find yourself trying to find fx(x) or fy (v), you are doing this the (very) hard way.)
Most questions answered within 3 hours.
-
Where is the error in this code sequence?
String s1 = "Hello";
String s2 = "ello";...
asked 10 months ago -
Financial data for Joel de Paris, Inc., for last year
follow:
Joel de Paris, Inc.
Balance...
asked 10 months ago -
Consider this reaction:
Al2(SO4)3 (aq)+ BaCl3
(aq) Al2Cl6 (aq)- +
3BaSO4(s) . What is the...
asked 10 months ago -
Suppose that Savneet is considering increasing her
recent random sample from 20 car rentals to 40...
asked 10 months ago -
Trucks arrive at an unloading terminal at an average rate of 120
per hour.
Trucks arrive...
asked 10 months ago -
Why are methanol and ethanol completely soluble in water while
octanol is not very little soluble....
asked 10 months ago -
A facilities manager at a university reads in a research report
that the mean amount of...
asked 10 months ago -
When the CuSO4 is rehydrated by adding water to the anhydrous
compound, is this an endothermic...
asked 10 months ago -
A ray of sunlight is passing from diamond into crown glass; the
angle of incidence is...
asked 10 months ago -
A block of mass 0.249 kg is placed on top of a light, vertical
spring of...
asked 10 months ago -
how do the kidneys compensate in the presences of acidosis
a) trigger hyperventilate
b) reserve acid...
asked 10 months ago -
Question 501 pts
The rental rate of capital to the firm increases. Which of the
following...
asked 10 months ago