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# Review of Terminology and Concepts

• Random variable: A variable that assumes values in a irregular pattern (or no particular pattern).
• Discrete random variables: Let X be a random variable. If the number of possible values of X is finite, or countably infinite, X is called a discrete random variable.

Let be all possible values of X, and be the probability that , then must meet the following conditions.

1. for all .

Examples: example 6.1 and 6.2 on p. 186

• Contineous random variables: If the values of X is an interval or a collection of intervals, then X is called a contineous random variable.

For contineous random variable, its probability is represented as

The function is called the probability density function (pdf) of the random variable , which has to meet the following condition.
1. for all .
2. .
3. if is not in .
Example 6.3 on page 187.

• Cumulative distribution function. The cumulative distribution function (cdf), denoted by , measures the probability that the random variable assumes a value less than or equal to , .
• If is discrete, then
• If is contineous, the

Some propertities of cdf include:

1. is a non-decreasing function. If then .
2. .
3. .

Example: 6.4, 6.5 on page 189.

• Expectation and variance. Expectation essentially is the expected value of a random variable. Variance is a measure how a random variable varies from its expected value.
• For discrete random variables

• For continueous random variables

• For discrete or continueous random variables, its variance is

which has an identity

• A more frequently used practical measure is standard deviation of a random variable, which is expressed as the same units as that of expectation.

Examples: 6.6, 6.7 on page 191.

• The mode. The mode is used to describe most frequently occured values in discreate random variable, or the maximum value of a continueous random variable.

Next: Useful Statistical Models Up: Statistical Model of Simulation Previous: Statistical Model of Simulation
Meng Xiannong 2002-10-18