CmpE 343 Lecture Notes 5: Discrete Distributions

When we toss a coin there are two outcomes and if the coin is fair, the two probabilities are equal. Consider the general case where the probability of heads is p0 and hence the probability of tails is 1−p0. This is the Bernoulli distribution where there are two outcomesX ∈ {0, 1}, and P{X = 1} = f(1) = p0 and P{X = 0} = f(0) = 1− p0 (3) When p0 = 1/2 we get the uniform distribution but with Bernoulli, the parameter p0 can take any value between 0 and 1. The two outcomes of 0 and 1 are generally named “failure” and “success” but Bernoulli distribution can denote any experiment with two outcomes, for example, a patient may live or die, it may rain tomorrow or not, a product may be defective or not, an email may be spam or not, and so on. The two cases of equation (3) can be written as P{X = x} = f(x; p0) = p x 0(1− p0) , x ∈ {0, 1} (4)