All Questions

Let $Y_1, \ldots, Y_n$ and $X_1, \ldots, X_n$ be i.i.d. $p$-Bernoulli random variables and let $T \in \{0, \ldots, n\}$ be a stopping time for the process. From Wald's equation, we know $$ E\left[\...

Let $X$ be a measurable space and let $P$ be a probability distribution on $X \times \{\pm 1\}$. Let $F$ be a function class on $X$, i.e., a collection of (measurable) functions from $X$ to $\mathbb R$...

Consider two sequences of (not necessarily independent) Bernoulli random variables $X_1, X_2, \ldots, X_n$ and $Y_1, Y_2, \ldots, Y_n$. Suppose that for any $i$, we have $\Pr[X_i = 1] = \Pr[Y_i = 1] = ...