Section 7 1 Discrete and Continuous Random Variables

Section 7. 1 Discrete and Continuous Random Variables AP Statistics January 5, 2009 Mr. Calise AP Statistics, Section 7. 1, Part 1

Random Variables A random variable is a variable whose value is a numerical outcome of a random phenomenon. n For example: Flip three coins and let X represent the number of heads. X is a random variable. n We usually use capital letters to denotes random variables. n AP Statistics, Section 7. 1, Part 1 2

Random Variables A random variable is a variable whose value is a numerical outcome of a random phenomenon. n For example: Flip three coins and let X represent the number of heads. X is a random variable. n The sample space S lists the possible values of the random variable X n AP Statistics, Section 7. 1, Part 1 3

Discrete Random Variable A discrete random variable X has a countable number of possible values. n For example: Flip three coins and let X represent the number of heads. X is a discrete random variable. n We can use a table to show the probability distribution of a discrete random variable. n AP Statistics, Section 7. 1, Part 1 4

Discrete Probability Distribution Table Value of X: x 1 x 2 x 3 … xn Probability: p 1 p 2 p 3 … pn AP Statistics, Section 7. 1, Part 1 5

Probability Distribution Table: Number of Heads Flipping 4 Coins TTTT TTTH TTHT THTT HTTT TTHH THTH HTHT THHTH HTT THHH HTHH HHTH HHHT HHHH X 0 1 2 3 4 P(X) 1/16 4/16 6/16 4/16 1/16 AP Statistics, Section 7. 1, Part 1 6

Discrete Probability Distributions n Can also be shown using a histogram AP Statistics, Section 7. 1, Part 1 7

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What is the average number of heads? AP Statistics, Section 7. 1, Part 1 9

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Continuous Random Variable n A continuous random variable X takes all values in an interval of numbers. AP Statistics, Section 7. 1, Part 1 11

Distribution of Continuous Random Variable AP Statistics, Section 7. 1, Part 1 12

Distribution of Continuous Random Variable The probability distribution of X is described by a density curve. n The probability of any event is the area under the density curve and above the values of X that make up that event. n AP Statistics, Section 7. 1, Part 1 13

Normal distributions as probability distributions n Suppose X has N(μ, σ) then we can use our tools to calculate probabilities. AP Statistics, Section 7. 1, Part 1 14

Assignment n Exercises: 7. 1 - 7. 11 AP Statistics, Section 7. 1, Part 1 15