Suppose that X and Y have the following joint probability density function. f (x, y) =...

Suppose that X and Y have the following joint probability density function. f (x, y) = (3/394)*y, 0 < x < 8, y > 0, x − 3 < y < x + 3

(a) Find E(XY). (b) Find the covariance between X and Y.

Expert Solution

Note-here everything is observed from graphical representation of joint pfd of X and Y. thus, graph is important

orchestra answered 1 year ago

Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y...

Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y (x,y) = 4x/y3 I(0.1)(x), I (1, ∞)(y). Calculate a) P(1/2 < X < 3/4, 0 < Y ≤ 1/3). b) P(Y > 5). c) P(Y > X).

Suppose X and Y have joint probability density function f(x,y) = 6(x-y) when 0<y<x<1 and f(x,y)...

Suppose X and Y have joint probability density function f(x,y) = 6(x-y) when 0<y<x<1 and f(x,y) = 0 otherwise. (a) Indicate with a sketch the sample space in the x-y plane (b) Find the marginal density of X, fX(x) (c) Show that fX(x) is properly normalized, i.e., that it integrates to 1 on the sample space of X (d) Find the marginal density of Y, fY(y) (e) Show that fY(y) is properly normalized, i.e., that it integrates to 1 on...

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the...

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the following estimator of the intercept of the Best Linear Predictor: A = ?̅ - B • ?̅ , where ?̅ is the sample mean of y, ?̅ is the sample mean of x, and B is the sample covariance of Y and X divided by the sample variance of X. Identify the probability limit of A (if any). For each step in your derivation,...

. The joint probability density function of X and Y is given by ?(?, ?) =...

. The joint probability density function of X and Y is given by ?(?, ?) = { ??^2? ?? 0 ≤ ? ≤ 2, 0 ≤ ?, ??? ? + ? ≤ 1 0 ??ℎ?????? (a) Determine the value of c. (b) Find the marginal probability density function of X and Y. (c) Compute ???(?, ?). (d) Compute ???(?^2 + ?). (e) Determine if X and Y are independent

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1 for 0 < x < 1, x < y < x + 1. What is the marginal density of X and Y? Use this to compute Var(X) and Var(Y) Compute the expectation E[XY] Use the previous results to compute the correlation Corr (Y, X) Compute the third moment of Y, i.e., E[Y3]

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1 for 0 < x < 1, x < y < x + 1. A. What is the marginal density of X and Y ? Use this to compute Var(X) and Var(Y). B. Compute the expectation E[XY] C. Use the previous results to compute the correlation Corr(Y, X). D. Compute the third moment of Y , i.e., E[Y3].

5. Suppose that X and Y have the following joint probability distribution: f(x,y) x 2 4...

5. Suppose that X and Y have the following joint probability distribution: f(x,y) x 2 4 y 1 0.10 0.15 2 0.20 0.30 3 0.10 0.15 Find the marginal distribution of X and Y. Find the expected value of g(x,y) = xy2 or find E(xy2). Find (x and (y. Find Cov(x,y) Find the correlations ρ(x,y) 3. The length of life X, in days, of a heavily used electric motor has probability density function Find the probability that the motor has...

Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0...

Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0 1 2 y 0 0.12 0.08 0.06 1 0.04 0.19 0.12 2 0.04 0.05 0.3 Find the followings: E(Y)= Var(X)= Cov(X,Y)= Correlation(X,Y)=

If the joint probability density function of the random variables X and Y is given by...

If the joint probability density function of the random variables X and Y is given by f(x, y) = (1/4)(x + 2y) for 0 < x < 2, 0 < y < 1, 0 elsewhere (a) Find the conditional density of Y given X = x, and use it to evaluate P (X + Y/2 ≥ 1 | X = 1/2) (b) Find the conditional mean and the conditional variance of Y given X = 1/2 (c) Find the variance...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value of k that makes this a probability density function. Compute the probability that P(X≤3/4, Y≥1/2). Find E(X). Find E(X|Y=y).

Question

Suppose that X and Y have the following joint probability density function. f (x, y) =...

Solutions

Expert Solution

Related Solutions

Suppose that the joint probability density function of ˜ (X, Y) is given by:´ f X,Y...

Suppose X and Y have joint probability density function f(x,y) = 6(x-y) when 0<y<x<1 and f(x,y)...

Suppose that we have two random variables (Y,X) with joint probability density function f(y,x). Consider the...

. The joint probability density function of X and Y is given by ?(?, ?) =...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

Consider a continuous random vector (Y, X) with joint probability density function f(x, y) = 1...

5. Suppose that X and Y have the following joint probability distribution: f(x,y) x 2 4...

Question 3 Suppose that X and Y have the following joint probability distribution: f(x,y) x 0...

If the joint probability density function of the random variables X and Y is given by...

Let X and Y have the following joint density function f(x,y)=k(1-y) , 0≤x≤y≤1. Find the value...