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 Posted: Tue, 8 May 2012 17:21:29 UTC
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Joined: Tue, 28 Feb 2012 21:22:24 UTC
Posts: 4
----The random variables X and Y are N(0,2) (Normal or Gaussian distributed) and independent. Find the PDF and CDF of Z = 2X + 3Y.

-------Two fair dice are rolled. Find the joint probability mass function of X and Y when X is the largest value obtained on any die and Y is the sum of the values.

------Given the joint PMF of X and Y as
Px,y(x,y)=
{1/4 (x,y)=(1,1) }
{1/4 (x,y)=(-1,1) }
{1/2 (x,y)=(0,0) }
{ 0 otherwise }
(a) Find E[X], E[Y], and E[XY],
(b) Show that X and Y are uncorrelated,
(c) Determine if X and Y are independent or not.

-------The joint density function of X and Y is
Fx,y(x,y)=
{ x+y 0<x<1.0<y<1
0 otherwise }

a) Are X and Y independent?
b) Find the density function of X?
c) Find P(X+Y < 1)=?

------Suppose the joint density function of X and Y is given by

Fx,y(x,y)=
{((e^-x/y) * (e^-y))/y 0<x<oo , 0<y<oo
0 otherwise }

a) Find the conditional density of x, given that Y=y.
b) Find P(X > 1 | Y = y).

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 Posted: Tue, 8 May 2012 17:42:01 UTC
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 Posted: Tue, 8 May 2012 17:47:15 UTC
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Joined: Tue, 28 Feb 2012 21:22:24 UTC
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 Posted: Tue, 8 May 2012 19:09:57 UTC
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