For f(x,y)=cxy, ? ≥ 0, ? ≥ 0, ? + ? ≤ 1, Determine E(Y|x) and...

For f(x,y)=cxy, ? ≥ 0, ? ≥ 0, ? + ? ≤ 1,
Determine E(Y|x) and E(X|y)

Expert Solution

orchestra answered 2 years ago

f(x,y)=30(1-y)^2xe^(-x/y). x>0. 0<y<1. a). show that f(y) the marginal density function of Y is a Beta...

f(x,y)=30(1-y)^2*x*e^(-x/y). x>0. 0<y<1. a). show that f(y) the marginal density function of Y is a Beta random variable with parameters alfa=3 and Beta=3. b). show that f(x|y) the conditional density function of X given Y=y is a Gamma random variable with parameters alfa=2 and beta=y. c). set up how would you find P(1<X<3|Y=.5). you do not have to do any calculations

f(x,y)=3(x+y) 0<x+y<1, 0<x<1, 0<y<1 (a) E(xy|x)=? (b) Cov(x,y)=? (c) x and y is independent? thank you!

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1,...

1 Let f(x, y) = 4xy, 0 < x < 1, 0 < y < 1, zero elsewhere, be the joint probability density function(pdf) of X and Y . Find P(0 < X < 1/2 , 1/4 < Y < 1) , P(X = Y ), and P(X < Y ). Notice that P(X = Y ) would be the volume under the surface f(x, y) = 4xy and above the line segment 0 < x = y < 1...

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is...

Given f(x,y) = 2 ; 0< x ≤ y < 1 a. Prove that f(x,y) is a joint pdf. b. Find the correlation coefficient of X and Y.

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2,...

Let f(x, y) be a function such that f(0, 0) = 1, f(0, 1) = 2, f(1, 0) = 3, f(1, 1) = 5, f(2, 0) = 5, f(2, 1) = 10. Determine the Lagrange interpolation F(x, y) that interpolates the above data. Use Lagrangian bi-variate interpolation to solve this and also show the working steps.

G1. Let f(x, y) = 1 for 0 < x < 1 and x < y...

G1. Let f(x, y) = 1 for 0 < x < 1 and x < y < (x + 1); and 0 otherwise. Find the correlation coefficient for this X and Y . (Hint: the answer is p (1/2) = 0.7071. See if you know all of the steps needed to get there.)

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a...

Let f(x) = a(e-2x – e-6x), for x ≥ 0, and f(x)=0 elsewhere. a) Find a so that f(x) is a probability density function b)What is P(X<=1)

f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1...

f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1 given X is the number of students who get an A on test 1 given Y is the number of students who get an A on test 2 find the probability that more then 90% students got an A test 2 given that 85 % got an A on test 1

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y...

Let the joint p.d.f f(x,y) = 1 for 0 <= x <= 2, 0 <= y <= 1, 2*y <= x. (And 0 otherwise) Let the random variable W = X + Y. Without knowing the p.d.f of W, what interval of w values holds at least 60% of the probability?

solve y' +(x+2/x)y =(e^x)/x^2 ; y(1)=0

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