Joint Probability Distributions

In summary, a joint probability distribution is a mathematical representation of the probabilities of two or more random variables occurring simultaneously. It takes into account the probabilities of multiple variables occurring together, and can be calculated by multiplying the individual probabilities of each variable. Joint probability distributions are important in statistics and data analysis, and can be extended to include any number of variables. However, as the number of variables increases, the calculations become more complex and may require advanced statistical techniques.
  • #1
Carla1985
94
0
I have this question:

View attachment 690and I'm a little confused. To calculate joint distributions in the earlier questions i was using:[TEX]P_{(\xi1,\xi2)}(x1,x2)=P_{(\xi1)}(x1)P_{(\xi2)}(x2)[/TEX]But that would mean that if:[TEX]P_{(\xi1,\xi2)}(2,0)=0\ either\ P_{(\xi1)}(2)=0\ or\ P_{(\xi2)}(0)=0[/TEX]which can't be true in either case as [TEX]P_{(\xi1,\xi2)}(1,0)\ isnt\ 0\ and\ neither\ is\ P_{(\xi1,\xi2)}(2,1)[/TEX]Can someone please explain what I'm missing. Thanks :/
 

Attachments

  • Screen Shot 2013-03-11 at 11.40.06 copy.jpg
    Screen Shot 2013-03-11 at 11.40.06 copy.jpg
    21.1 KB · Views: 51
Physics news on Phys.org
  • #2
Nevermind, I found my mistake. This was only for independent variables, which these obviously aren't :)
 

FAQ: Joint Probability Distributions

What is a joint probability distribution?

A joint probability distribution is a mathematical representation of the probabilities of two or more random variables occurring simultaneously. It shows the likelihood of different combinations of values for the variables.

How is a joint probability distribution different from a marginal distribution?

A joint probability distribution takes into account the probabilities of multiple variables occurring together, while a marginal distribution only considers the probabilities of one variable at a time.

How do you calculate the joint probability distribution?

The joint probability distribution can be calculated by multiplying the individual probabilities of each variable occurring in a given combination. For example, if the probability of variable A is 0.5 and the probability of variable B is 0.6, the joint probability of A and B occurring together is 0.5 * 0.6 = 0.3.

What is the importance of joint probability distributions?

Joint probability distributions are important in statistics and data analysis as they allow us to understand the relationships between multiple variables and make more accurate predictions. They are also used in various fields such as finance, engineering, and social sciences.

Can joint probability distributions be used for more than two variables?

Yes, joint probability distributions can be extended to include any number of variables. This is known as a multivariate joint probability distribution. However, as the number of variables increases, the calculations become more complex and may require advanced statistical techniques.

Similar threads

I Poisson distribution with conditional probability
Replies
3
Views
3K
"The Chase" Quiz Show -- probability of being caught by the Chaser
Replies
1
Views
2K
Joint probability of partitioned vectors
Replies
2
Views
1K
I Can Exact Joint Probability Distributions Predict Violations in CHSH Tests?
Replies
14
Views
2K
MHB Joint Probability Density from two Gaussian Distributions
Replies
1
Views
2K
Joint probability distribution of two images
Replies
1
Views
6K
Determine marginal distribution of random vector on unit sphere
Replies
9
Views
1K
Joint Probability Distr. of 2 Non-Independent Variables Given Marginals
Replies
5
Views
3K
Adiabatic approximation for joint probability distribution
Replies
2
Views
3K
What Is the Distribution of the First Failure Time for Two Independent Machines?
Replies
4
Views
5K

Hot Threads

Recent Insights

Back
Top