# Statistics: Probability Distributions

**Random Variable: **All possible outcomes of a random experiment are random variables. A random variable set is denoted by *X*.

# Discrete Distributions

## Bernoulli Distribution

We have a single trial (only one observation) and 2 possible outcomes. For example, flipping a coin. Let’s say we accept *True* for heads. Then if the probability of getting heads is *p,* the probability of the opposite situation is* 1-p.*

## Binomial Distribution

Bernoulli was for a single observation. More than one Bernoulli observations create a binomial distribution. For example, tossing a coin several times in a row.

Trials are independent of each other. The result of one attempt does not affect the next.

The binomial distribution can be expressed as *B(n, p )*. *n *is the number of trials and* p* is the probability of success.