Thread: Help with bivariate distribution?

1. Help with bivariate distribution?

Suppose the sample space of the random variables X and Y is 0 < x < 1 and $\displaystyle x^2$ < y < 1. Let f (x, y) = c on this sample space, and 0 elsewhere.
(a) Sketch the sample space.
This is a bivariate distribution so it's a table with an X axis from 0 to 1 but i'm not sure about the y-axis?

(b) Determine the constant c.
does the probability always add up to one?

(c) Calculate $\displaystyle f_X$ (x) and $\displaystyle f_Y$ (y)
(d) Are X and Y independent?
(e) Find P (X > Y )

2. Originally Posted by Statsnoob2718
Suppose the sample space of the random variables X and Y is 0 < x < 1 and $\displaystyle x^2$ < y < 1. Let f (x, y) = c on this sample space, and 0 elsewhere.
(a) Sketch the sample space.
This is a bivariate distribution so it's a table with an X axis from 0 to 1 but i'm not sure about the y-axis?

(b) Determine the constant c.
does the probability always add up to one?

(c) Calculate $\displaystyle f_X$ (x) and $\displaystyle f_Y$ (y)
(d) Are X and Y independent?
(e) Find P (X > Y )
(a) The random variables are continuous not discrete. The sample space is all points in the region bounded by the y-axes, the line y = 1 and the curve y = x^2.

(b) Integrate the f(x, y) over the sample space and set the integral equal to 1. Then solve for c.

(c) Apply the definitions and do the necessary calculations.

(d) Does f(x, y) = f(x) f(y)?

(e) Integrate f(x, y) over an appropriate region of the sample space.

If you need more help, please post all your work and say where you get stuck.

3. The rvs are dependent by inspection, since < y < 1
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