Help with joint distributions?

In summary, joint distributions are a type of probability distribution that shows the probability of different combinations of values for two or more variables occurring together. They are important because they allow us to analyze the relationship between multiple variables and understand how they affect each other. The main difference between joint and marginal distributions is that joint distributions describe the relationship between variables while marginal distributions show the probability of a single variable occurring. Joint distributions are calculated by multiplying the probabilities of each variable occurring together and are commonly used in various fields such as statistics, economics, and psychology to make predictions and understand the relationships between different variables.
  • #1
slaux89
5
0

Homework Statement


Suppose X and Y have joint density f(x,y)=2 for 0<y<x<1. Find P(X-Y>z)

According to the textbook the answer should be (1-z)[tex]^{2}[/tex]/2

Homework Equations





The Attempt at a Solution



[tex]\int[/tex] [tex]\int[/tex] 2dxdy

for x=[0, z+y] and y=[0,1]

=[tex]\int[/tex] 2(z+y) dy

=2z+1

since we are only interested in the values where y<x, we divide this by half to get

z+ 1/2

I'm clearly way off from the answer I'm suppose to get, so I would like to know where it is I went wrong. thanks!
 
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  • #2
Nevermind, I got it now!
 

FAQ: Help with joint distributions?

What are joint distributions?

Joint distributions are a type of probability distribution that describes the relationship between two or more random variables. It shows the probability of different combinations of values for the variables occurring together.

Why are joint distributions important?

Joint distributions are important because they allow us to analyze the relationship between multiple variables and understand how they affect each other. This is useful in many fields of science, such as statistics, economics, and psychology.

What is the difference between joint distributions and marginal distributions?

Joint distributions describe the relationship between multiple variables, while marginal distributions describe the probability distribution of individual variables. In other words, joint distributions show how variables are related, while marginal distributions show the probability of a single variable occurring.

How are joint distributions calculated?

Joint distributions are calculated by multiplying the probabilities of each variable occurring together. This is also known as the joint probability function. The resulting values are then organized into a table or graph to show the relationship between the variables.

What are some applications of joint distributions?

Joint distributions have many applications in science and research. They are commonly used in fields such as data analysis, risk assessment, and market research. They can also be applied in areas such as genetics, ecology, and engineering to understand the relationship between different variables and make predictions based on their probabilities.

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