Does anyone know a good proof that:

I have a thing for infinite product representations of things, and I've finally found a way of factoring the real fixed point of cosine. Here's my method: Start with a guess. The “best” guess is 3/4 apply newton's method for cos(x)=x, but only for a...

Ok, just one more question before my final tomorrow: Do there exist non-zero compact multiplier operators on L^2[0,1]? I want to say yes, and I want to try the operator Mf(x) = xf(x), because we've done a little bit with it in the past. However,...

Consider the two-dimensional (non-negative) random variable (X,Y), where Y = a + bX + cX^2 + εX, and where εX is a random variable having E(εX) = 0 and Var(εX)=σ2x. 1. What is E(Y|X) and Var(Y|X)? 2. Suppose X is normally distributed with E(X) = μ'...

I need to know if this conditional statement is necessarily true: If A is a non-empty set bounded below, then ∀δ>0 ∃x∈A in [inf A, inf A + δ)?