Bernoulli Distribution

A random variable X has a Bernoulli distribution with parameter p if it can assume a value of 1 with a probability of p and the value of 0 with a probability of (1-p). The random variable X is also known as a Bernoulli variable with parameter p and has the following probability mass function:

The mean of a random variable X that has a Bernoulli distribution with parameter p is

E(X) = 1(p) + 0(1-p) = p

The variance of X is

EX. A random variable whose value represents the outcome of a coin toss (1 for heads, 0 for tails, or vice-versa) is a Bernoulli variable with parameter p, where p is the probability that the outcome corresponding to the value 1 occurs. For an unbiased coin, where heads or tails are equally likely to occur, p = 0.5.