Calculating the marginal density function

[stgermaine]

Homework Statement

Let f(x,y) = 24xy where x=[0,1], y=[0,1], x+y=[0,1]
Find E[X] and E[Y]

Homework Equations

E[X] = the integral from neg. infinity to positive infinity of x * f_X(x) dx where f_X is the marginal density function of X.

The Attempt at a Solution

f_X is found by integrating f(x,y) in terms of dy over the span of neg. infinity to positive infinity.

For the integral, I used the boundaries 0 and 1. Solution guides online suggest that the marginal density function f_X is equal to 24x.

 

[Ray Vickson]

Homework Statement

Let f(x,y) = 24xy where x=[0,1], y=[0,1], x+y=[0,1]
Find E[X] and E[Y]

Homework Equations

E[X] = the integral from neg. infinity to positive infinity of x * f_X(x) dx where f_X is the marginal density function of X.

The Attempt at a Solution

f_X is found by integrating f(x,y) in terms of dy over the span of neg. infinity to positive infinity.

For the integral, I used the boundaries 0 and 1. Solution guides online suggest that the marginal density function f_X is equal to 24x.

So, what did YOU get for f_X(x)? Show all your work.

RGV