Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find...

Given the joint probability density function f(x ,y )=k (xy+ 1) for 0<x <1--and--0<y<1 , find the correlation--ROW p (X,Y) .

Expert Solution

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).

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).

Given the joint density function of X and Y as fX,Y(x,y) = cx2 + xy/3 0...

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. 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

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

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4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation...

4. The joint density function of (X, Y ) is f(x,y)=2(x+y), 0≤y≤x≤1 . Find the correlation coefficient ρX,Y . 5. The height of female students in KU follows a normal distribution with mean 165.3 cm and s.d. 7.3cm. The height of male students in KU follows a normal distribution with mean 175.2 cm and s.d. 9.2cm. What is the probability that a random female student is taller than a male student in KU?

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.

Let X and Y have joint pdf f(x,y)=k(x+y), for 0<=x<=1 and 0<=y<=1. a) Find k. b)...

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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...

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]

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