discrete uniform distribution
binomial distribution
negative binomial distribution

discrete uniform distribution

f(x;k) = 1/k

these are conveniently represented with bar charts

example is a die which each x has probability = 1/6

the mean and the variance are the standard definitions: mean is the sum of all
k over x sub-i so it's simply k. the mean is the expectation which is also
similarly derived.

the bernoulli process

1. only 2 outcomes
2. consists of n trials
3. probability of success is constant from trial to trial
4. the repeated trials are independent

binomial random variable: the number of X successes in n Bernoulli trials
binomail distribution: the probability distribution of the binomail random
variable
the denotation of the binomial distribution is b(x;n,p)
x: number of successes
n: number of trials
p: probability of each success

there is also the equation for its computing: (n choose x)(p^(x))(q^(n-x))

(n choose x)(p^(x))(q^(n-x)) can be written to express the probability
distribution instead of drawing the values in a table

binomial experiment

1. only 2 outcomes b)

negative binomial

negative binomial random variable
negative binomial random distribution