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Sections 4.1 and 4.2

PROBABILITY DISTRIBUTIONS. This chapter will deal with the construction of probability distributions by combining the methods of Chapter 2 with the those of Chapter 3.Probability Distributions will describe what will probably happen instead of what actually did happen.. COMBINING DESCRIPTIVE MET

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Sections 4.1 and 4.2

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    1. Sections 4.1 and 4.2 Overview Random Variables

    2. PROBABILITY DISTRIBUTIONS

    3. COMBINING DESCRIPTIVE METHODS AND PROBABILITIES

    4. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS A random variable is a variable (typically represented by x) that has a single numerical value, determined by chance, for each outcome of a procedure. A probability distribution is a graph, table, or formula that gives the probability for each value of a random variable.

    5. EXAMPLES

    6. SAMPLE SPACE FOR ROLLING A PAIR OF DICE

    8. DISCRETE AND CONTINUOUS RANDOM VARIABLES A discrete random variable has either a finite number of values or a countable number of values, where “countable” refers to the fact that there might be infinitely many values, but they can be associated with a counting process. A continuous random variable has infinitely many values, and those values can be associated with measurements on a continuous scale in such a way that there are no gaps or interruptions.

    9. EXAMPLES Let x be the number of cars that travel through McDonald’s drive-through in the next hour. Let x be the speed of the next car that passes a state trooper. Let x be the number of As earned in a section of statistics with 15 students enrolled.

    10. PROBABILITY HISTORGRAM

    11. EXAMPLES

    12. REQUIREMENTS FOR A PROBABILITY DISTRIBUTION

    13. EXAMPLES

    14. MEAN, VARIANCE, AND STANDARD DEVIATION

    15. Enter values for random variable in L1. Enter the probabilities for the random variables in L2. Run “1-VarStat L1, L2” The mean will be . The standard deviation will be sx. To get the variance, square sx. FINDIND MEAN, VARIANCE, AND STANDARD DEVIATION WITH TI-83/84 CALCULATOR

    16. ROUND-OFF RULE FOR µ, s, AND s2

    17. MINIMUM AND MAXIMUM USUAL VALUES

    18. EXAMPLE

    19. IDENTIFYING UNUSUAL RESULTS USING PROBABILITIES Rare Event Rule: If, under a given assumption the probability of a particular observed event is extremely small, we conclude that the assumption is probably not correct. Unusually High: x successes among n trials is an unusually high number of successes if P(x or more) is very small (such as 0.05 or less). Unusually Low: x successes among n trials is an unusually low number of successes if P(x or fewer) is very small (such as 0.05 or less).

    20. EXAMPLE

    21. EXPECTED VALUE

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