I have two questions:
Let A~N(mu,sigma), B~U(0,θ) and C=A*B
1.What is the distribution of the product of a normal and uniform matrices, C? (How we can prove it)
2.What statistical properties of these two matrices are preserved in their product? (I understand, for example, if both matrices have normal distribution, their product will preserves their euclidean distance and their inner product, but that s not the case when one matrix is uniform).