- #1
Dustinsfl
- 2,281
- 5
Homework Statement
If ##X\sim\mathcal{U}(-1,1)## and ##Y = X^2##, is it possible to determine to ##cov(X, Y)##?
Homework Equations
\begin{align}
f_x &=
\begin{cases}
1/2, & -1<x<1\\
0, & \text{otherwise}
\end{cases}\\
f_y &=
\begin{cases}
1/\sqrt{y}, & 0<x<1\\
0, & \text{otherwise}
\end{cases}
\end{align}
The Attempt at a Solution
$$
cov(X,Y) = E[XY] - E[X]E[Y] = E[XY] - 0\cdot 1/2 = E[XY]
$$
Now
$$
E[XY] = \int_0^1\int_{-1}^1g(X, Y)f_{x,y}(x,y)dxdy
$$
From the information that I have, can I determine ##E[XY]##?