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!