Phox said:Homework Statement
Let X and Y be random variables of the continuous type having the join p.d.f.:
f(x,y) = 8xy, 0<=x<=y<=1
Find the marginal pdf's of X. Write your answer in terms of x.
Find the marginal pdf's of X. Write your answer in terms of x.
Homework Equations
The Attempt at a Solution
f1(x) = integral(8xy)dy from 0 to 1
f2(y) = integral(8xy)dx from 0 to 1
f1(x) = 4x
f2(x) = 4y
This isn't right. what am I doing wrong?
Phox said:I've graphed it. I'm not sure what this tells me
A joint probability density function (PDF) is a mathematical function that describes the probability of two or more random variables occurring simultaneously. It shows the likelihood of a specific combination of values for the variables.
A joint PDF describes the probability of multiple variables occurring together, while a marginal PDF describes the probability of a single variable occurring on its own. In other words, a joint PDF considers all variables, while a marginal PDF focuses on one variable at a time.
To calculate a marginal PDF from a joint PDF, you simply integrate the joint PDF over all the other variables except the one you are interested in. This removes the other variables and leaves you with the marginal PDF for the variable of interest.
A joint PDF is useful when you need to analyze the relationship between multiple variables and their combined probabilities. A marginal PDF is useful when you only need to focus on one variable at a time.
Yes, a joint PDF can have any number of variables. However, as the number of variables increases, the complexity of the function and the calculations also increase. Therefore, it is more common to see joint PDFs with two or three variables.