# Shared Flashcard Set

## Details

Discrete Distributions
Discrete Probability Distributions
19
Mathematics
02/16/2013

Term
 Probability Distribution of a random variable
Definition
 The probability distribution of a random variable X is a description of the probabilities associated with the possible values of X. For a discrete random variable, the distribution is often specified by just a list of the possible values along with the probability of each.   In some cases, it is convenient to express the probability in terms of a formula.
Term
 Probability of a Discrete Variable X with possible values x1, x2,..., Xn...
Definition
Term
 The cumulative distribution function of a discrete random variable X, denoted as F(x), is
Definition
 [image]
Term
 The mean, expected value, variance and standard deviation of a discrete random variable X is:
Definition
 [image]
Term
 What is a discrete Uniform Function?
Definition
 [image]
Term
 Mean of a discrete uniform random variable X:
Definition
Term
 Mean of X when X is a discrete uniform random variable on the consequtive integers a, a+1, a+2, .....b for a less than or equal to b
Definition
 [image]
Term
 Binomial Distribution
Definition
 [image]
Term
 The mean and variance of a binomial random variable
Definition
 [image]
Term
 Geometric probability distribution function
Definition
 [image]
Term
 The mean and variance of a geometric distribution
Definition
 [image]
Term
 Negative Binomial Distribution
Definition
 A generalization of a geometric distribution in which the random variable is the number of Bernoulli trials required to obtain r successes results in the negative bionmial distribution
Term
 Probability Distribution Function of a negative binomial distribution:
Definition
 [image]
Term
 Mean and Variance of a binomial distribution function
Definition
 [image]
Term
 Probability function of Hypergeometric distribution ( samples are selected without replacement)
Definition
 [image]
Term
 Mean and Variance of a Hypergeometric distribution
Definition
 [image]
Term
 For a hypergeometric random variable, E(x) is similar to the mean a binomial random variable. Also, V(x) differs from the result for a binomial random variable only by the term shown below.
Definition
 [image]
Term
 Function of Poisson probability distribution
Definition
 [image]
Term
 Mean and Variance of Poisson distribution function:
Definition
 [image]
Supporting users have an ad free experience!