# joint distribution

1. ### Joint Distribution

Hi everyone, I've got a problem with a joint probability density function question. Given f(x, y) = e^-(x+y), 0 <= x < ∞ , 0 <= y < ∞ , and 0 otherwise I need to verify that f is a valid joint PDF. The fact that f(x, y) >= 0 for all x, y is obvious. However I'm having trouble with...
2. ### Continuous joint entropy with fully dependent variable

Consider a variable X with a continuous uniform distribution in the interval [a,b] and a variable Y that is fully dependent on X, i.e., p(Y=y | X=x)=δ(x=y), where δ is a delta distribution with peak x. What is the entropy H(X,Y) of the joint distribution? Intuitively, samples from the joint...
3. ### integrating joint probability distribution

Hi, could you help me in compute the integral with respect to x of f(x,y)d(x,y) where f(x,y) is a joint probability distribution? I know that the integral with respect to x of f(x,y)dx is just f(y) where f(y) is the marginal distribution of y, but in the exercise I have f(x,y)d(x,y) inside the...
4. ### The avarage age problem

Hi Guys, I’m trying to figure out a good model for modeling the average age of a population. More specifically the average number of years people have been enrolled at a university who are in turn members of a club, which I call “age”. • The rate at which new members arrive could be...
5. ### Joint PDF of X and a Function Y = g(X)

Thakur here, My question is regarding the joint pdf of the input and output of a system. Lets say I have a system represented by a deterministic function Y = g(X). Lets say X is uniformly distributed. I know I can find pdf of Y "p(y)" using standard textbook techniques. However, is it...
6. ### Joint distribution from multiple marginals

Consider an experiment consisting of a repeated trial with two random Bernoulli (=binary) variables, A and B. Each trial consists of multiple outcomes for both A and B. Each trial has the same number of samples and the underlying joint distribution of A and B is the same everywhere. Of course...
7. ### max sum

Consider two discrete variables x and y each having three possible states, for example x, y ∈ { 0, 1, 2 } . Construct a joint distribution p(x, y) over these variables having the property that the value  xi that maximizes the marginal p(x), along with the value  yi that maximizes the...
8. ### Approximate Bayesian Computation and joint posteriors

Hi! I am performing Approximate Bayesian Computation (ABC) in phylogenetic research. I have a few questions for which I am looking for a useful answer (as I am a biologist, but not a statistician). (1) How can I combine the posterior distributions of several ABC runs? I need to calculate...
9. ### Combining two dependant discrete random variables

Hi, I’m looking for a way to combine two discrete random variables (which I have as probability distributions). The combination should be the product (or other operation) of the two variables. This would be easy if they were independent, but they’re not. There is a known correlation between...
10. ### Joint distribution from marginals (unknown conditional) distributions

Hi, This is my first post in this forum; I hope someone can help me with this --thanks in advance for reading! I'm trying to find the joint probability distribution of two variables where I only know their marginal probability distributions. More specifically, I'm interested in the joint...
11. ### Need help with joint distribution involving cauchy distributions

Okay so I know that help is only given to those who show effort, but I'm totally stuck on this one, I don't even know where to start. I know what the Cauchy distribution is and i could plug it in for the Y variables, but I don't know where that would get me. Please help me out!