I am being haunted about this problem on the value of the determinent of this Random Matrix ever since it came into my mind last week.The problem goes like this:
Suppose $A$ is a square matrix of order $n$ whose elements are uniformly and independently chosen from the interval $[a,b]$ where both $a$ and $b$ are positive. If $X$ is the r.v. corresponding to $\det A$ then what about the following :
(1)The $\min$ and $\max$ of $X$.
(2)The probability distribution of $X$.
If the case for the matrices of order $n$ seems too complicated/laborious I will be grateful for the solutions for $n=2$ and $n=3$.Am eagerly waiting !Thank you in advance!