I have a question that is critical to my work, but I am not sure if it is any possible. Assume that you have two uniform random variables X and Y. The product distribution of Z=XY is not a uniform. What should the distributions of X and Y be to have Z a uniform distribution. Following this, can we construct an outer product of X and Y to generate a uniformly distributed matrix X . Y^T?
Note: We can we also use modulo arithmetic. It would be better if all are integers, if not consider them real. I need to understand the potential of this.
Please help and Thank you all :)