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Probability Distributions

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Probability Density function, Probability distribution, and Probability

Could someone give me definitions with examples of each.

Please make the explanations as clear as possible.

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Solution Preview

Let's start with the last term you listed above.

Probability is a way to quantify how likely some event is going to happen. It is always expressed as a number between 0 and 1, inclusive. A probability of 0 indicates no chance of occurrence, whereas a probability of 1 indicates sure occurrence.

Probability distribution is a function that maps events to their probability of occurrence. We can consider 2 cases -- first, in the discrete case (where events are indexed by values like 1, 2, 3, ...), the probability distribution is also called the probability mass function (pmf), and takes the form P(X = k) = p, where p is the probability of X = k. On the other hand, we have the ...

Solution Summary

Solution includes detailed descriptions of each, as well as how to use probability density functions and probability distributions.