Two Variables

Often, we are concerned with the joint behavior of two random variables. We may describe such behavior in terms of a joint distribution (density function) such as p(x, y). As suggested before, if such a distribution is partitionable, as p(x, y) = g(X)h(y) (11.18)

then the two variables x and y are independent.

Example. We may develop a simple joint distribution when tossing two dice, where each die represents a random-variable generator. The probability of obtaining any given pair of numbers, say, 3 and 5 [a 3 on the ''X' die and a 5 on the "Y" die is P(X, Y) = P(3, 5)]. For any given pair, of which there are 36 possibilities, the probability is clearly 1/36. Therefore, this is a uniform discrete joint distribution that has only one value, namely, P(X, Y) = 1 /36.

There is also a mean or expected-value concept when dealing with a joint distribution. This may be expressed as

As might be expected, if x and y are independent, the preceding yields the product of the expected, or mean, values of the individual distributions.

Project Management Made Easy

Project Management Made Easy

What you need to know about… Project Management Made Easy! Project management consists of more than just a large building project and can encompass small projects as well. No matter what the size of your project, you need to have some sort of project management. How you manage your project has everything to do with its outcome.

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