So for my weekly homework assignment for my probability class, there is a question that I am unsure about.
Typically, a question usually begins with something along the lines of "Suppose X and Y are random variables with joint density..." and asks to find something along the lines of "find the marginal density of X."
Now that's all fine and good; it's easy enough to do. What i'm confused about is a similar question that begins in a similar fashion, but instead asks "find the probability density function of X."
My main concern is this: is there a difference between the marginal density and probability density? are they the same thing? It is confusing because the question still involves a joint density function of X and Y.
If there is a need for clarification on my question let me know and i'll try to create an example that is not my exact homework problem because that wouldn't encourage my learning.
Thanks!
$\endgroup$ 21 Answer
$\begingroup$If you have a random vector $(X, Y)$ then its joint density is a function of two arguments connected with joint probability function $\text{Pr} (X \leq x, Y \leq y)$.
But if you know the joint density of $(X, Y)$ you're able to compute the density of $X$ or $Y$ themselves - these densities of single variables are called marginal ones.
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