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Probability Distributions

Probability Density function, Probability distribution, and Probability

Could someone give me definitions with examples of each.

Please make the explanations as clear as possible.

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.