= Bernoulli process
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{title2=$B_n\overset{\mathrm{iid}}\sim\operatorname{Bernoulli}(p)$}
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A Bernoulli process is a sequence of <independent and identically distributed random variables> with a <Bernoulli distribution>: $\mathbb P(B_n=1)=p$ and $\mathbb P(B_n=0)=1-p$. It models repeated <Bernoulli trials> with a fixed success <probability> and no dependence between trials. The count $K_n=\sum_{j=1}^nB_j$ has a <binomial distribution>, <expected value> $np$, and <variance> $np(1-p)$; the first success time has a <geometric distribution> on $\{1,2,\ldots\}$. The observations $B_n$ and the accumulated count $K_n$ are different <stochastic processes>: the observations are independent, while consecutive counts share all earlier observations. https://ocw.mit.edu/courses/6-436j-fundamentals-of-probability-fall-2018/b9342e718ec4c58d98ec97dcfcb0d56e_MIT6_436JF18_lec20.pdf[MIT, The basics of stochastic processes, section 2]{ref}
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