All Questions

In all what follows, let $\mathcal{P}(\mathbb{R}^n)$ denote the set of probability measures on $(\mathbb{R}^n, \mathcal{B}(\mathbb{R}^n))$ and $\mathcal{C}_n$ the set of $n \times n$ correlation ...

Given two stochastic processes, $X[n]$ and $Y[n]$, both being WSS (wide state stationary) and independents. What would be the Average and Autocorrelation function of $Z[n] = Y[n] X[n]$? Is the ...

Suppose I have x red and y blue balls. At each timestep I draw a ball with probability $$P(\text{red ball}) = (x/(x+y))^z, P(\text{blue ball}) = 1-P(\text{red ball})$$ where z is fixed. Each ball is ...

Consider a strictly stationary process $X_t$, $t\in\mathbb{Z}_{\geq 1}$. Could you help me to disprove the following statement: "For $t, s > 0$, the bivariate vectors $(X_s, X_t)$ and $(X_t, ...