**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.

The distribution shows an increased probability of an increase in the number of successful outcomes.

*p:* the probability of success,*n:* number of trials*q:* the probability of failure* (1-p).*

## Uniform Distribution

All outcomes have the same probability of success. Rolling a dice, 1 to 6.

## Poisson Distribution

It is a distribution related to the frequency at which the outcome of an event occurs in a given time interval.

*Po(λ), λ* is the excepted events in the specified time interval. **It is the known average of the events happening in that time interval**. *X* is the number of times the event happened in the specified time…