Show that there are 70 different Bernoulli random variables of parameter 1/2 that can be defined on Ω.
2026-03-26 16:57:01.1774544221
Consider the probability space Ω = {0, 1}^ 3 with equally likely outcomes.
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Since each of the outcomes is equally likely, Bernoulli random variables of parameter $\frac{1}{2}$ correspond to subsets of $\Omega$ of size $4$ ($|\Omega| = 8$). There are $\binom{8}{4} = 70$ such subsets, so there are $70$ such Bernoulli random variables.