- #1

semidevil

- 157

- 2

## Homework Statement

A)

Suppose that (X; Y ) is uniformly chosen from the set given by 0 < X < 3 and x < y < root(3x). Find the marginal density fy (y) of Y.

B)

If X is uniformly distributed on [0, 2], and given that X = x, Y is uniformly distributed on [x 2x], what is P[Y <2]?

**2. The attempt at a solution**

For A), to find the joint density, I integrate 1 dy dx of the shape to get the area. the joint density is then 1/area. This makes sense to me.

For B), integrating 1 dydx doesn't seem to work and instead, it is just simply combining f(x) and f(y). 1/2 * 1/x to get the density.

I understand the uniform shortcuts so I know where 1/2 and 1/x came from, but how do I know when to use which method? I,e. how do I know that I need to integrate 1, rather then just multiply f(x)*f(y).

both tell us that x, y are uniformly distributed; I understand that the difference is that one involves a conditional distribution, so is that the determining factor?

**3. Relevant equations**

if f(x) is uniform on (a,b), the area is b-a. the density would then be 1/(b-a).

f(x)*f(y) = f(x,y) if independent.