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Unifrom distribution of a disc

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rosh300
#1
Oct28-09, 01:13 PM
P: 17
1. The problem statement, all variables and given/known data

[tex]\D = \{(x,y) \in \mathbb{R}^2 | x^2 + y^2 \leq 1\} [/tex] i.e. a disc or radius 1.
Write down the pdf f_{xy} for a uniform distribution on the disc.

2. Relevant equations



3. The attempt at a solution

[tex] f_{xy} = \frac{(x^2 + y^2)}{\pi} \mbox{for} x^2 + y^2 \leq 1[/tex] 0 otherwise
as the area of the disc pi and to make it uniform you divide by pi so the probability integrates to 1
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gabbagabbahey
#2
Oct28-09, 02:25 PM
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gabbagabbahey's Avatar
P: 5,003
Hmmm...

[tex] f_{xy} = \frac{(x^2 + y^2)}{\pi}[/tex]

Doesn't look very uniform to me
rosh300
#3
Oct28-09, 03:17 PM
P: 17
i think i got it: its [tex]
f(x,y)_{xy} = \left\{ \begin{array}{rl}
\frac{1}{\pi} &\mbox{for } x^2 + y^2 \leq 1\\
0 &\mbox{otherwise}
[/tex]

thanks

gabbagabbahey
#4
Oct28-09, 03:25 PM
HW Helper
gabbagabbahey's Avatar
P: 5,003
Unifrom distribution of a disc

Looks good to me!
lordslytherin
#5
Oct26-10, 03:20 PM
P: 5
I am doing a some practice questions for stats and i tried to integrate this to get 1 but i can't so what are the appropriate limits and how would i go about finding the marginal distribution of x and y? Thanks


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