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:
4 3 2 1 0
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. Therand function 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
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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