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Probability Distributions - Lesson Summary

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The key points from this module are:

Association between Random Variables - Joint Probability

The Joint Probability distribution of X and Y labeled as p(x, y) gives the probability of events of the form X=x and Y=y. This represents the simultaneous outcome of both the random variables.

Correlation and Dependence

Dependency: A variable whose value depends on the value assigned to another variable.

Correlation: The relationship between two or more variables is considered as correlation.

Independent and Identically Distributed(IID)

Identically Distributed means that there are no overall trends –the distribution doesn’t fluctuate and all items in the sample are taken from the same probability distribution.

Independent means that the sample items are all independent events. In other words, they aren’t connected to each other in any way.

The Binomial Distribution is used when there are exactly two mutually exclusive outcomes of a Bernoulli Trial. These outcomes are appropriately labeled "success" and "failure".

Normal Distribution

A Normal Distribution comes with a perfectly symmetrical shape. This means that the distribution curve can be divided in the middle to produce two equal halves. The symmetric shape occurs when one-half of the observations fall on each side of the curve.