"Horse sense is what keeps horsesfrom betting on what people will do."

7.1 DISCRETE AND CONTINUOUS RANDOM VARIABLES(Pages 367 - 380)

OVERVIEW: When the outcomes of anevent that produces random results are numerical, the numbersobtained are called random variables. The sample space for the eventis just a list containing all possible values of the random variable.This section introduces the concept of a random variable and theprobabilities associated with the various values of thevariable.

**Random variable**: Theoutcome of a random phenomenon.

**Discrete random variables**

Example: If a coin is flipped fourtimes, then the number of heads obtained (five possible values:0,1,2,3,4) is a discrete random variable, x, with probabilities asindicated:

TTHH

THHT

THHH

THTH

TTTH

HTHH

HTHT

TTHT

HHTH

HTTH

THTT

HHHH

HHHT

HHTT

HTTT

TTTT

X

43210Probability

1/16

4/16

6/16

4/16

1/16

A **continuous randomvariable** takes all values in an intervalof numbers. (A continuous random variable has associated with it adensity curve.)

Example: If x is a random number inthe interval [0,1], then x is a continuous random variable. The

randfunction onthe TI-83 generates values of x in the interval [0,1]. In this case,prob(x=.5) = 0 and prob(x>.5) = 1/2. With continuous randomvariables, the distinction between > and >= can be ignored. Atechnical note is that the random numbers generated on the TI-83 arerounded to 10 decimal places, so you are really looking atdiscrete.

Very common types of continuous random variablesare represented in normal probability distributions. You can generaterandom observations from a normal distribution with your TI-83. Forinstance, **randNorm(**

randNorm( 50,4,100)->L _{1}SortA(L _{1})

A reminder that these commands will result in asorted list of random numbers from a normal population with mean = 50and standard deviation = 4.

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