📘 probability theory

1. **Problem Statement:** We are given a stochastic process $\{N(t): t \geq 0\}$ which is a Poisson process. We need to determine if the statement "$N(t)$ has independent and non-s

1. **State the Central Limit Theorem (CLT):** The CLT states that for a sequence of independent and identically distributed (IID) random variables $X_1, X_2, \ldots, X_n$ with mean

1. The problem is to write the formula for $f_x(x)$ as given in the image. 2. The formula involves an integral and sums with exponential and characteristic function terms.