Dependent Bernoulli trials with same probability of success?

Question

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 :).

Any example will be fine. But preferably a simple one, as I am not good at probability theory :) — Kenneth, Jul 09 '21 at 07:16

score 1 · Accepted Answer · answered Jul 09 '21 at 13:15

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.

Dependent Bernoulli trials with same probability of success?

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