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I am not that good at probability theory.

My need: I need a simple example of a series of Bernoulli trials with the same probability of success in each trial, but where the Bernoulli trials are dependent.

Thanks for considering my request :).

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  • $\begingroup$ In what sense are they dependent, or will any example do? $\endgroup$
    – Henry
    Commented Jul 9, 2021 at 7:11
  • $\begingroup$ Any example will be fine. But preferably a simple one, as I am not good at probability theory :) $\endgroup$
    – Kenneth
    Commented Jul 9, 2021 at 7:16

1 Answer 1

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Consider $X \sim Ber(p)$ for $p \in [0,1]$. Define a sequence of random variables $Y_{i}, i = 1, \ldots, n$ by $Y_{1} = Y_{2} = \ldots = Y_{n} = X$

Then each $Y_{i}$ is Bernoulli with probability of success $p$, but they are all equal to each other and thus dependent.

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