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Asked: 2026-06-09T07:29:09+00:00

So, let’s say we have a random variable X over {0,1}^1. That means that

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So, let’s say we have a random variable X over {0,1}^1. That means that X can take the value 0 or it can take the value 1. My question is, why isn’t this probability precisely 1/2 as it would be in the uniform distribution? In other words, why can’t we say anything about the probability distribution of X knowing that it can only take two values, and the value that it does take (either 0 or 1 in this case) is random?

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  1. Editorial Team

    You are describing bernoulli distribution, which is also Binomial distribution with n=1.

    For this distribution your parameter is usually p – the probability of getting 1.

    The probability of getting 1 and 0 varies, and might not be the same.

    If you have p=1/2 – it is a specific (very useful case) where the “experiment” is unbiased, and is often used for statistical tests – for testing if a certain data set is biased or not.

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