Uniform distribution of a disc

[mathmathmad]

Homework Statement

Consider a disc of radius 1 in the plane D in R
D = {(x,y) in R | x^2+y^2 <= 1}
write the marginal pdf of x and y

Homework Equations

The Attempt at a Solution

so the joint pdf is 1/Pi for x^2 + y^2 <= 1 <- correct?
but how to I get the marginal pdfs?

 

[statdad]

You have

<br /> f(x,y) = \frac 1 \pi<br />
as the joint density. As in every case the marginal density of one variable is found by integrating out the other. Suppose you want the marginal density of x - you need to integrate out y.

<br /> g(x) = \int_a^b \frac 1 \pi \, dy<br />

The question is: what should you use for the limits a and b?
Draw the unit circle and see the set of y-values that are possible when x is fixed.

 

[mathmathmad]

a=0
b=sqrt (1 - x^2) ?

 

[statdad]

a=0
b=sqrt (1 - x^2) ?

Try again. Did you draw the picture?

 

[mathmathmad]

a = - sqrt (1 - x^2)
b = sqrt (1 - x^2)

or should it be -1 to 1