Question

Let the random variables X and Y have joint cdf as follows:

F(x,y) = {1-e^-4x-e^-5y+e^-4x-5y, x>0, y>0

0, otherwise

Find the correlation coefficient of X and Y

Answer #1

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1. Let (X,Y ) be a pair of random variables with joint pdf given
by f(x,y) = 1(0 < x < 1,0 < y < 1).
(a) Find P(X + Y ≤ 1).
(b) Find P(|X −Y|≤ 1/2).
(c) Find the joint cdf F(x,y) of (X,Y ) for all (x,y) ∈R×R.
(d) Find the marginal pdf fX of X. (e) Find the marginal pdf fY
of Y .
(f) Find the conditional pdf f(x|y) of X|Y = y for 0...

Let (X, Y ) have joint cdf F, and let G be the cdf of the random
variable X + Y . Show that F(x, x) ≤ G(2x) for all x ∈ R

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f(x,y) = y/144 if 0 < 4x < y < 12 and
0 otherwise
Find Cov (X,Y).

Let X and Y be two continuous random variables with joint
probability density function f(x,y) = xe^−x(y+1), 0 , 0< x <
∞,0 < y < ∞ otherwise
(a) Are X and Y independent or not? Why?
(b) Find the conditional density function of Y given X = 1.(

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f(x,y) =
6x 0<y<1, 0<x<y,
0 otherwise.
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c) Find the conditional density of X given Y = 1 /2

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3. Find the marginal means for both random variables.
4. Find the marginal variances for both random variables.
5. Find the correlation of X and Y .
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