Probability Index

Probability is used to estimate the likely-hood of an event. Probabilities are always non-negative and sum to one.

Notation

Random Variable | Notation

In probability a random variable is denoted using capital latin letters usually X, Y, and Z or A, and B respectively.

Probability Distribution | Notation

A probability distribution is denoted like a function. Often a capital P is used for the function name, and the capital letter X is used for the argument to the function.

Conditional Probability | Notation

Conditional probability is denoted using a vertical bar between the two variables

Joint Distribution | Notation

A joint probability distribution is denoted like a function often using P as the function name. The capital letters X and Y are often used to represent the random variables of the distribution and are arguments to the function.

Expected Value | Notation

The expected value of a probability distribution is denoted as the function E(X).

Arithmetic Mean | Notation

The arithmetic mean of a data set is denoted by a horizontal bar over the variable x.

N Choose R Combination | Notation

The number of possible ways to choose r combinations from n total items is denoted using two parentheses with the n value above the r value. A subscript p or c is used to denote whether it is a combination or permutation.

N Choose R Permutation | Notation

The number of possible ways to choose r permutations from n total items is denoted using two parentheses with the n value above the r value. A subscript p or c is used to denote whether it is a combination or permutation.

Population Mean | Notation

Meaningful description here.

Standard Deviation | Notation

Meaningful description here.

Variance | Notation

Meaningful description here.

Formulas

Combination | Formula

The combination formula describes the possible combinations of r elements out of a group of n elements where order does not matter.

Permutation | Formula

The permutation formula describes the possible permutations of r elements out of a group of n elements where order does matter.

Permutations of Set | Formula

The number of permutations of n distinct items is given by n factorial. A permutation is a unique ordering or arangment of the set of items.

Arithmetic Mean | Formula

The arithmetic mean, also called the sample mean, is the average of a sample space. To calculate the arithmetic mean sum all the data points in a sample space and then divide by the number of elements.

Conditional Probability | Formula

The conditional probility formula shows how to calculate the probability of a event B, given that another event A has already occured.

Expected Value Continuous Distribution | Formula

The expected value, describes the most likely value of a probability distribution. It also describes where a probability distribution is centered.

Expected Value Discrete Distribution | Formula

To calculate the expected value of a discrete distribution multiply all of the events of the distribution with the probability of the element occuring.

Standard Deviation | Formula

The sample standard deviation formula is denoted by the greek lower case sigma symbol in the case of the population and the latin letter s for the sample.

Concepts

Random Variable | Concept

A random variable represents an event whose outcome is unknown.

Bayes Theorem | Concept

Bayes theorem describes a way of expressing conditional probability.

Examples

N Choose R Order Does Not Matter | Example

To calculate n choose r where order does not matter you can use the formula for four choose two combinations.

N Choose R Order Matters | Example

To calculate n choose r where order matters you can use the permuation formula.

Number of Permutations for N Distinct Items | Example

To calculate the possible permutations of n distinct items, you can take the factorial of n to get the numer of permutations.

Population Mean of Continuous Distribution | Example

The population mean, sometimes called the expected value, describes where a probability distribution is centered.

Population Mean of Discrete Distribution | Example

The population mean, sometimes called the expected value, describes where a probability distribution is centered.

Variance of Discrete Distribution | Example

Variance measures how spread out a distribution is.