Statistics & Probability

Correlation coefficients measure the strength of association between two variables. The most common correlation coefficient, called the Pearson product-moment correlation coefficient , measures the strength of the linear association between variables. In this tutorial, when we speak simply of a correlation coefficient, we are referring to the Pearson product-moment correlation. Generally, the correlation coefficient of a sample is denoted by r , and the correlation coefficient of a population is denoted by ρ or R . How to Interpret a Correlation Coefficient The sign and the absolute value of a correlation coefficient describe the direction and the magnitude of the relationship between two variables. The value of a correlation coefficient ranges between -1 and 1. The greater the absolute value of a correlation coefficient, the stronger the linear relationship. The str

The probability of a sample point is a measure of the likelihood that the sample point will occur. Probability of a Sample Point By convention, statisticians have agreed on the following rules. The probability of any sample point can range from 0 to 1. The sum of probabilities of all sample points in a sample space is equal to 1. Example 1 Suppose we conduct a simple statistical experiment. We flip a coin one time. The coin flip can have one of two outcomes - heads or tails. Together, these outcomes represent the sample space of our experiment. Individually, each outcome represents a sample point in the sample space. What is the probability of each sample point? Solution: The sum of probabilities of all the sample points must equal 1. And the probability of getting a head is equal to the probability of getting a tail. Therefore, the probability of each sample point (heads or tails) must be equal to 1/2. Example 2 Let's repeat the experiment

To understand probability distributions, it is important to understand variables. random variables, and some notation. A variable is a symbol ( A , B , x , y , etc.) that can take on any of a specified set of values. When the value of a variable is the outcome of a statistical experiment, that variable is a random variable . Generally, statisticians use a capital letter to represent a random variable and a lower-case letter, to represent one of its values. For example, X represents the random variable X. P(X) represents the probability of X. P(X = x) refers to the probability that the random variable X is equal to a particular value, denoted by x. As an example, P(X = 1) refers to the probability that the random variable X is equal to 1. Probability Distributions An example will make clear the relationship between random variables and probability distributions. Suppose you flip a coin two times. This simple statistical experiment can have

Often, we want to compute the probability of an event from the known probabilities of other events. This lesson covers some important rules that simplify those computations. Definitions and Notation Before discussing the rules of probability, we state the following definitions: Two events are mutually exclusive or disjoint if they cannot occur at the same time. The probability that Event A occurs, given that Event B has occurred, is called a conditional probability . The conditional probability of Event A, given Event B, is denoted by the symbol P(A|B). The complement of an event is the event not occuring. The probability that Event A will not occur is denoted by P(A'). The probability that Events A and B both occur is the probability of the intersection of A and B. The probability of the intersection of Events A and B is denoted by P(A ∩ B). If Events A and B are mutually exclusive, P(A ∩ B) = 0. The probability tha