# Discrete Probability Distribution

Random Variable

a variable whose values are determined by chanc

Discrete Variable

have a finite number of possible values or an infinite number of values that can be counted.

Continuous Variable

variables that can assume all values in the interval between any two given values

Expected Value

theoretical average of the variable; 𝜇 = 𝐸(𝑋) = ∑ 𝑋 ∙ 𝑃(𝑋)

Fixed number of trialsEach trial can have only two outcomes or outcomes that can be reduced to two outcomesOutcomes on each trial must be independentProbability of success must remain the same

Four requirements of binomial experiment

Binomial Distribution

The outcomes of a binomial experiment and the corresponding probabilities of these outcomes

Binomial Probability Formula

Define the following quantities.n = the number of repeated trialsp = the probability of success on any given trialq = 1−p=the probability of failure on any given triala = the number of successes that occur

discrete probability distribution

a listing of all the possible outcomes of an experiment for a discrete random variable along with the relative frequency of each outcome

Mean and standard deviation of binomial probability

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