Question

Exercise 10.45. Suppose that the joint distribution of X,Y is bivariate normal with parameters σX,σY,ρ,µX,µY as...

Exercise 10.45. Suppose that the joint distribution of X,Y is bivariate normal with parameters σX,σY,ρ,µX,µY as described in Section 8.5. (a) Compute the conditional probability density of X given Y =y. (b) Find E[X|Y].

Homework Answers

Answer #1

I HAVE CHANGED THE NOTATIONS A BIT ..

IF U FACE ANY ISSUE DO LET ME KNOW IN THE COMMENTS

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Let X and Y have a bivariate normal distribution with parameters μX = 0, σX =...
Let X and Y have a bivariate normal distribution with parameters μX = 0, σX = 3; μY = 8, σY = 5; ρ = 0.6. Find the following probabilities. P(-6 < X < 6) P(6 < Y < 14 | X = 2)
Let X and Y have a bivariate normal distribution with parameters μX = 0, σX =...
Let X and Y have a bivariate normal distribution with parameters μX = 0, σX = 3; μY = 8, σY = 5; ρ = 0.6. Find the following probabilities. (A) P(-6 < X < 6) (B) P(6 < Y < 14 | X = 2)
The joint probability density function of X and Y is bivariate normal with E(X)=E(Y)=0, sd(x)=sd(y)=9, and...
The joint probability density function of X and Y is bivariate normal with E(X)=E(Y)=0, sd(x)=sd(y)=9, and correlation coefficient is 0. Find: (a) P(X=<6, Y=<12); (b) P(X^2+Y^2=<36)
Using a normal probability distribution with µx = 37 and σx = 3.5, find each probability....
Using a normal probability distribution with µx = 37 and σx = 3.5, find each probability. Illustrate each situation using appropriate z-scores. Draw the normal curve and be sure to show the inflection points.(a) P(x ≤ 32) (b) P(35 ≤ x ≤ 38) (c) P(x ≥ 42)
MARIGINAL AND JOINT DISTRIBUTIONS The joint distribution of X and Y is as follows. Values of...
MARIGINAL AND JOINT DISTRIBUTIONS The joint distribution of X and Y is as follows. Values of Y 1 0 P{X=x} Values of X 1 0.1 0.2 0.3 0 0.3 0.4 0.7 P{Y=y} 0.4 0.6 1.0 a. Find the marginal distribution of X and Y. b. Find the conditional distribution of X given y = 1 c. Compute the conditional expectation of Y given X=1, E{Y=y|X=1}
Suppose that the joint density function of X and Y  is given by f (x, y)  ...
Suppose that the joint density function of X and Y  is given by f (x, y)  =  45 xe−3x(y + 5)     x  >  0, y  >  0. (a) Find the conditional density of  X, given Y  =  y. (b) Find the conditional density of Y, given  X  =  x. (c) Find P(Y  >  5 | X  =  4).
The joint probability distribution of two random variables X and Y is given in the following...
The joint probability distribution of two random variables X and Y is given in the following table X Y → ↓ 0 1 2 3 f(x) 2 1/12 1/12 1/12 1/12 3 1/12 1/6 1/12 0 4 1/12 1/12 0 1/6 f(y) a) Find the marginal density of X and the marginal density of Y. (add them to the above table) b) Are X and Y independent? c) Compute the P{Y>1| X>2} d) Compute the expected value of X. e)...
Given the joint probability density function f ( x , y ) for 0 < x...
Given the joint probability density function f ( x , y ) for 0 < x < 3 and 0 < y < 2 x^2y/81 Find the conditional probability distribution of X=1 given that Y = 1 f ( x , y ) = x^2 y/ 81 . F i n d the conditional probability distribution of X=1 given that Y = 1. i . e . f (X ∣ y = 1 )( 1 )
Suppose that the joint probability density function of the random variables X and Y is f(x,...
Suppose that the joint probability density function of the random variables X and Y is f(x, y) = 8 >< >: x + cy^2 0 ≤ x ≤ 1, 0 ≤ y ≤ 1 0 otherwise. (a) Sketch the region of non-zero probability density and show that c = 3/ 2 . (b) Find P(X + Y < 1), P(X + Y = 1) and P(X + Y > 1). (c) Compute the marginal density function of X and Y...
STAT 120 Suppose that X have a gamma distribution with parameters a = 2 and θ=...
STAT 120 Suppose that X have a gamma distribution with parameters a = 2 and θ= 3, and suppose that the conditional distribution of Y given X=x, is uniform between 0 and x. (1) Find E(Y) and Var(Y). (2) Find the Moment Generating Function (MGF) of Y. What is the distribution of Y?