# Discrete Random Variable

Given , a discrete random variable,

Population Mean (Expectancy)

Population Variance

If two discrete random variables $X$ and $Y$ are independent,

# Bernoulli Distribution

If success, . If failure, .

# Binomial Distribution

$X = $ number of successes in independent repetitions of the experiment.

Define as the th repetition’s success or not. follows a Bernoulli Distribution.

# Geometric Distribution

$X = $ number of tries up to and including first success

Let

Given

Such that

Using the same method as above,

# Poisson Distribution (To be continued…)

Poisson Distribution is essentially a binomial distribution with very large $n$ (very small time interval).