missmathematica
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Joint distr of (X,Y) is f(x,y)=c(x^2+y^2) for 0<=x,y<=1 (0 otherwise); find c, ...
Hey! I have this following problem to solve:
The joint distribution of the random variable pair (X, Y) is the following:
. . . . .\(\displaystyle f(x,\, y)\, =\, c\, (x^2\, +\, y^2)\)
for \(\displaystyle 0\, \leq\, x\, \leq\, 1,\, 0\, \leq\, y\, \leq\, 1,\) and 0 otherwise.
a) Determine the constant c and the distributions of the random variables X and Y.
b) Are the random variables X and Y independent?
c) Determine the conditional distribution X | Y = 1, and the conditional expectionation E(X | Y = 1).
I have got that c = 2/3 by integrating, is that right? But how should I continue?
Thank you for your help!
Hey! I have this following problem to solve:
The joint distribution of the random variable pair (X, Y) is the following:
. . . . .\(\displaystyle f(x,\, y)\, =\, c\, (x^2\, +\, y^2)\)
for \(\displaystyle 0\, \leq\, x\, \leq\, 1,\, 0\, \leq\, y\, \leq\, 1,\) and 0 otherwise.
a) Determine the constant c and the distributions of the random variables X and Y.
b) Are the random variables X and Y independent?
c) Determine the conditional distribution X | Y = 1, and the conditional expectionation E(X | Y = 1).
I have got that c = 2/3 by integrating, is that right? But how should I continue?
Thank you for your help!
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