For example, in the first roll in the game of craps (roll a pair of dice) the events of interest are: the sum of upfaces is 2, or 3, or 4, ... , or 12. Hence, there are only 11 events of interest. If we let

As another problem, reconsider the urn problem where the urn contained 30 blue balls and 50 red balls and that 3 of these balls were selected at random without replacement. Recall we wanted to determine the probability that all the balls were of the same color. Just let

The **range** of a random variable is the set of values it can assume. For example in the game of craps, the range of *X* is {2, 3, ... ,12} while in the urn problem, the range of *X* is {0, 1, 2, 3}. As another example, let *X *be the height of an adult male in inches. It is hard, even, impossible to come up with minimum or maximum of *X *; hence,
a convenient range is the interval
.
This seems odd at first, but keep in mind we are trying to *model* height. Actually the best model of height employs a range of
.
We will discuss this later.

Essentially, random variables come in two types: **discrete** and **continuous** random variables . A discrete random variable has a finite (or listable) range. The range of a continuous random variable is an interval of numbers. In the first two examples, the random variables are discrete while in the last example on height, the random variable is continuous.

- 1.
- Let X denote the number of aces in a 2 card hand drawn without replacement fro a standard deck 0f 52 cards. What is the range of X? Is it discrete or continuous?
- 2.
- In the last problem, let Y denote the average area of the two dealt cards. Assume that we can measure area infinitely precise. What is the range of Y? Is it discrete or continuous?
- 3.
- In the urn problem discussed above, let Z denote the number of red balls in the sample (without replacement) of size 3. What is the range of Z? Is it discrete or continuous?
- 4.
- Let X denote the temperature at noon in Kalamazoo in centigrade. What is the range of X? Is it discrete or continuous?
- 5.
- Let X denote the number of people in a queue at a bank teller's window. What is the range of X? Is it discrete or continuous?