EDA CHAP3

discrete distribution

describes the probability of occurrence of each value of a discrete random variable

discrete random variable

is a random variable that has countable values, such as a list of non-negative integers.

discrete probability distribution

each possible value of the discrete random variable can be associated with a non-zero probability. Thus, it is often presented in tabular form.

random variable

is a variable whose value is subject to variations due to chance (i.e. randomness, in a mathematical sense). As opposed to other mathematical variables, a ——- conceptually does not have a single, fixed value (even if unknown); rather, it can take on a set of possible different values, each with an associated probability

Probability Histogram:

This histogram displays the probabilities of each of the three discrete random variables. The formula, table, and probability histogram satisfy the following necessary conditions of discrete probability distributions:

Probability Mass Function

This shows the graph of a probability mass function. All the values of this function must be non-negative and sum up to 1.

Cumulative Distribution Functions

discrete

random variable is one whose set of possible values is finite.

continous

random variable is one that can assume values on a continuous scale.

PROABILITY DISTRIBUTION OF DISCRETE RANDOM VARAIBLES

A probability distribution is a formula or a table listing of all possible values that a random variable can take on. This is the theoretical counterpart of frequency distribution.

COMULATIVE DISTRIBUTION FUNCTION (CDF)

Total probility of all values up to and including a given number.

Cumulative probabilities

, P(X <= x) where X still represents the random variable and x now represents an upper ilmit, are found by adding individual probabilities.

EXPECTED VALUES OF RANDOM VARIABLES

X, denoted by E(X), is equal to the weighted average of the elements x in the support S, where each element is weighted by its respective probability. Use the following formula:

binomial experiment

is a statistical experiment that has the following properties:

binomial random variable

the number of successes x in n repeated trials of a binomial experiment

binomial distribution

The probability distribution of a binomial random variable is called a ——-

binomial probability

refers to the probability that a binomial experiment results in exactly x successes

Cumulative Binomial Probability

refers to the probability that the binomial random variable falls within a specified range (e.g., is greater than or equal to a stated lower limit and less than or equal to a stated upper limit).

Poisson distribution

is the probability distribution that results from a Poisson experiment.

Poisson experiment

is a statistical experiment that has the following properties:

 The experiment results in outcomes that can be classified as successes or failures.

 The average number of successes (μ) that occurs in a specified region is known.

 The probability that a success will occur is proportional to the size of the region.

 The probability that a success will occur in an extremely small region is virtually zero

Poisson random variable

is the number of successes that result from a Poisson experiment.

Poisson distribution

The probability distribution of a Poisson random variable is called a ——

cumulative Poisson probability

refers to the probability that the Poisson random variable is greater than some specified lower limit and less than some specified upper limit.