A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5]...

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5]

(a) What is the value of the constant c?

(b) Are X and Y independent? Explain.

(c) What is the covariance oc X and Y? i.e. Cov(X ,Y)

Expert Solution

orchestra answered 2 years ago

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1)....

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1). a) Determine the value of C b) Determine the marginal distribution of X and compute E(X) and Var(X) c) Determine the marginal distribution of Y and compute E(Y) and Var(Y) d) Compute the correlation coefficient between X and Y

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤...

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤ y ≤ 1. (i) Find the conditional means of X given Y, and Y given X. (ii) Find the conditional variance of X given Y. (iii) Find the correlation coefficient between X and Y.

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Are X and Y independent or dependent? Why or why not? 2. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 3. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 4....

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x + y), x =0, 1, 2, y = 0, 1, with y ≤ x. 1. Find g(x | y) and draw a figure depicting the conditional pmfs for y =0 and 1. 2. Find h(y | x) and draw a figure depicting the conditional pmfs for x = 0, 1 and2. 3. Find P(0 < X <2 |Y = 0), P(X ≤ 2 |Y...

Question 6. Suppose the joint pdf of X and Y is f(x,y) = ax^2y for 0...

Question 6. Suppose the joint pdf of X and Y is f(x,y) = ax^2y for 0 < x < y 0 < y < 1 0 otherwise Find a. Find the correlation between X and Y. Are X and Y independent? Explain. Find the conditional variance Var(X||Y = 1)

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and...

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and y=1,2 calculate the covariance of x and y calculate the correlation coefficient of x and y Thank you

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0 < x, 0 < y, x + y < 2 and 0 otherwise 1) Find P[X ≥ 1|Y ≤ 1.5] 2) Find P[X ≥ 0.5|Y ≤ 1]

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x <...

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x < infinity and 0 < y < infinity with parameters λ > 0 and μ > 0 a) Find c such that this is a PDF. b) Show that X and Y are Independent c) What is P(1 < X < 2, 0 < Y < 5) ? Leave in exponential form d) Find the marginal distribution of Y, f(y) e) Find E(Y)

Let X and Y be two jointly continuous random variables with joint PDF f(x,y) = Mxy^2...

Let X and Y be two jointly continuous random variables with joint PDF f(x,y) = Mxy^2 0<x<y<1 a) Find M = ? b) Find the marginal probability densities. c) P( y> 1/2 | x = .25) = ? d) Corr (x,y) = ?

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i)...

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i) find the marginal pdf of X and Y respectively, ii) the conditional pdf of Y given x, that is fY|X(y|x), iii) E(Y|x) and Corr(X,Y).

Question

A joint pdf is defined as f(x) =cxy for x in [1,2] and y in [4,5]...

Solutions

Expert Solution

Related Solutions

The joint PDF of X and Y is given by f(x, y) = C, (0< x<y<1)....

Let X and Y have the joint pdf f(x, y) = 8xy, 0 ≤ x ≤...

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Let the joint pmf of X and Y be defined by f (x, y) = c(x...

Question 6. Suppose the joint pdf of X and Y is f(x,y) = ax^2y for 0...

let the random variables x and y have the joint p.m.f f(x,y)= (x+y)/12 where x=1,2 and...

Let X and Y be continuous random variables with joint pdf f(x, y) = kxy^2 0...

Let X and Y have joint PDF f(x) = c(e^-(x/λ + y/μ)) 0 < x <...

Let X and Y be two jointly continuous random variables with joint PDF f(x,y) = Mxy^2...

let the continuous random variables X and Y have the joint pdf: f(x,y)=6x , 0<x<y<1 i)...