4, This is also illustrated in Fig. 1. The rv X defines a function from the sample space to the real numbers. It has the domain n = {u 1 , ... , u6 } and the range {I, 2, 4}. 0 Example 2. Measuring a Physical Constant When a physical constant is measured, we may let X be the value obtained. Because of errors of measurement, X may deviate from the true value of the constant.

In how many ways can a sequence of n elements be drawn without replacement from the given set of N elements? If N = 3 and n = 2, the number of ways is equal to 6, viz. AlA2' AlA3' A 2A l , A 2A 3, A3 A l' A 3A 2· Generally, the number of ways can be found in the following way. 7. Some Theorems in Combinatorics second position, and so on; finally, there remain N - n + 1 elements to choose from in the nth position. The total number of ways is the product of these numbers, that is, N(N - 1)· ... · (N - n + 1).

Over the points 0, 1, ... , respectively. This picture of a distribution of a rv is of great value for grasping the idea of a rv. In the sequel, we will therefore occasionally speak of the "mass" or "probability mass" of a discrete rv. 5. 5. Some Discrete Distributions We shall present some discrete distributions in a list which is useful for reference, but is perhaps hard to absorb at first reading. The most important of these distributions are the binomial distribution, the hypergeometric distribution and the Poisson distribution.