285%2Bchap04-P1

285%2Bchap04-P1 - Statistics Chapter 4 Random Variables and...

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Chap 5-1 Statistics Chapter 4 Random Variables and Probability Distributions – Discrete Sections 4.1-4.4
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Chap 5-2 Introduction to Probability Distributions Random Variable Represents a possible numerical value from a random event Takes on different values based on chance Random Variables Discrete Random Variable Continuous Random Variable Ch. 5 Ch. 6
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Chap 5-3 A discrete random variable is a variable that can assume only a countable number of values Many possible outcomes: number of complaints per day number of TV’s in a household number of rings before the phone is answered Only two possible outcomes: gender: male or female defective: yes or no spreads peanut butter first vs. spreads jelly first Discrete Random Variable
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Chap 5-4 Continuous Random Variable A continuous random variable is a variable that can assume any value on a continuum (can assume an uncountable number of values) thickness of an item time required to complete a task temperature of a solution height, in inches These can potentially take on any value, depending only on the ability to measure accurately.
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Chap 5-5 Discrete Random Variables Can only assume a countable number of values Examples: Roll a die twice Let x be the number of times 4 comes up (then x could be 0, 1, or 2 times) Toss a coin 5 times. Let x be the number of heads (then x = 0, 1, 2, 3, 4, or 5)
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Chap 5-6 Probability Distributions for Discrete Random Variables 2 Requirements that must be satisfied ( 29 ( 29 = 1 0 x p x p for all values of x Where the summation of p(x) is over all possible values of x 1. 2.
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Chap 5-7 Experiment: Toss 2 Coins. Let x = # heads. T T Discrete Probability Distribution 4 possible outcomes T T H H H H Probability Distribution 0 1 2 x x Value Probability 0 1/4 = .25 1 2/4 = .50 2 1/4 = .25 .50 .25 Probability
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Chap 5-8 A list of all possible [ x i , P(x i ) ] pairs x i = Value of Random Variable (Outcome) P(x i ) = Probability Associated with Value x i ’s are mutually exclusive (no overlap) x i ’s are collectively exhaustive (nothing left out) 0 P(x i ) 1 for each x i Σ P(x i ) = 1 Discrete Probability Distribution
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Chap 5-9 Mean of Discrete R. V.
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This note was uploaded on 03/23/2011 for the course STATS 100 taught by Professor Lawerence during the Spring '11 term at Rutgers.

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285%2Bchap04-P1 - Statistics Chapter 4 Random Variables and...

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