Probability: Random Sample Problem I need some help on the following problem:
Let $X_1$ and $X_2$ be random sample from the pdf
\begin{equation}
f(x) = \begin{cases}
4x^3,&0<x<1\\
0, & \text{otherwise}
\end{cases}
\end{equation}
Obtain $P(X_1X_2\geq 1/4)$.
So here is what I did:
$P(X_1X_2\geq 1/4)=1-P(X_1X_2< 1/4)$
Next, I need to obtain the distribution of $X_1X_2$ in order to evaluate the above probability, but how? I really appreciate if you could give me a solution on this.

The distribution of $X_1X_2$ is $f(x,y)=16x^3y^3$, where I've used $x$ for $X_1$ and $y$ for $X_2$. The limits are just $0<x,y<1$ as before.
