Joint and Marginal Distributions

Nd787 C4 L01 A10 Joint And Marginal Distributions V1

Summary of Terms

Joint Distribution - The joint distribution p(x,y) gives the probability of event x and event y happening. This idea can be generalized to situations with more than two random variables as well.

Marginal Distribution - The marginal distribution of a subset of random variables gives the probability distribution over just the variables in that subset.

For example, let's say you know the probability distribution on a vehicle's x,y,z location in space: p(x,y,z), but you only care about the vehicle's altitude (z). You could compute the marginal distribution for z by integrating out the other two variables.

p(z) = \int_{-\infty}^{\infty} \int_{-\infty}^{\infty} p(x,y,z) dx dy

Independence - Two events x and y are independent when their joint probability is equal to the product of the individual probabilities. That is, when:

p(x,y) = p(x)p(y)

Want to read more?

The wikipedia articles on these topics are pretty helpful if you want to read more!

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