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You simply have a function with two (or more) arguments which are continuous.
For example, z = p(x,y) would be a surface in 3 dimensions where x and y are the values taken by the two variables, X and Y respectively, and z is the probability associated with them.
w = g(x,y,z) would be a hyper-surface in 4-dimensional space and so on.
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How do you calculation joint probability?
You have a function with two arguments (inputs). After that, the calculations depend on whether or not the two random variables are independent. If they are then the joint distribution is simple the product of the individual distribution. But if not, you have some serious mathematics ahead of you!
What is marginal probability?
Suppose you have two random variables, X and Y and their joint probability distribution function is f(x, y) over some appropriate domain. Then the marginal probability distribution of X, is the integral or sum of f(x, y) calculated over all possible values of Y.
Discuss distribution function of mixed random variable?
In some situationsX is continuous but Y is discrete. For example, in a logistic regression, one may wish to predict the probability of a binary outcome Y conditional on the value of a continuously-distributed X. In this case, (X, Y) has neither a probability density function nor a probability mass function in the sense of the terms given above. On the other hand, a "mixed joint density" can be defined in either of two ways:Formally, fX,Y(x, y) is the probability density function of (X, Y) with respect to the product measure on the respective supports of X and Y. Either of these two decompositions can then be used to recover the joint cumulative distribution function:The definition generalizes to a mixture of arbitrary numbers of discrete and continuous random variables.
What is the conditional expectation function?
It is the integral (or sum) of the joint probability distribution function of the two events, integrated over the domain in which the condition is met.
Example of joint probability?
Joint probability is the probability that two or more specific outcomes will occur in an event. An example of joint probability would be rolling a 2 and a 5 using two different dice.
