Statistics

Statistics

probability outcome of a single coin toss. There are two outcomes to this experiment; the coin might come up heads with probability p or it may come up tails with probability 1-p.

• Binomial distribution: This type of distribution is used to describe the number of successes within a given series of events that are independent. A classic example and application of this distribution is the measurement of outcomes in a Yes/No experiment, where the outcomes yes versus no, have the same probability of success. • Poisson binomial distribution: This is very similar to the above binomial distribution. However, it is the measurement of outcomes in a Yes/No experiment, where the outcomes yes versus no, have a different probability of success. • Poisson distribution: Not to be confused with Poisson binomial distribution, this measures a large number of individual unlikely events that happen within a certain time interval. Think of two events that are not likely to happen at the same time. • Normal distribution: This distribution is often times referred to as the Gaussian or bell curve. In this distribution, each variable can be measured as the sum of many smaller independent variables. For this, recall how average class grades are often expressed as a bell curve. Each individual grade becomes part of the bell. • Chi-squared distribution: This distribution measures the sum of the squares of N= the number of observations ) of independent Gaussian random variables. Gaussian means normally distributed, and example of this would be a bell curve. • F- distribution: This is the distribution uses the chi-squared distribution. The F-distribution is the measurement of the ratio of two (normalized) random variables that experience chi- squared distribution. This is commonly used in the analysis of variance.

• Exponential distribution: This distribution is used to describe the time between consecutive events that are random in a random, non-reoccurring process.

• Students t-distribution: This distribution is used in the measurement and estimation of unknown means from Gaussian (normally distributed) populations.

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