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Section 7.1 Discrete and Continuous Random Variables AP Statistics www.toddfadoir.com/apstats Random Variables A random variable is a variable whose value is a numerical outcome of a random phenomenon. For example: Flip three coins and let X represent the number of heads. X is a random variable. We usually use capital letters to denotes random variables. 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. For example: Flip three coins and let X represent the number of heads. X is a random variable. The sample space S lists the possible values of the random variable X AP Statistics, Section 7.1, Part 1 3 Discrete Random Variable A discrete random variable X has a countable number of possible values. For example: Flip three coins and let X represent the number of heads. X is a discrete random variable. We can use a table to show the probability distribution of a discrete random variable. AP Statistics, Section 7.1, Part 1 4 Discrete Probability Distribution Table Value of X: x1 x2 x3 … xn Probability: p1 p2 p3 … 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 HTTH HTHT THHT HHTT 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 Can also be shown using a histogram AP Statistics, Section 7.1, Part 1 7 AP Statistics, Section 7.1, Part 1 8 What is the average number of heads? x 0 1 2 3 4 1 16 6 16 4 16 0 16 32 16 2 4 16 12 16 12 16 4 16 1 16 4 16 AP Statistics, Section 7.1, Part 1 9 Continuous Random Variable A continuous random variable X takes all values in an interval of numbers. AP Statistics, Section 7.1, Part 1 10 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. The probability of any event is the area under the density curve and above the values of X that make up that event. AP Statistics, Section 7.1, Part 1 13 Normal distributions as probability distributions Suppose X has N(μ,σ) then we can use our tools to calculate probabilities. AP Statistics, Section 7.1, Part 1 14 Assignment Exercises: 7.1 - 7.18 AP Statistics, Section 7.1, Part 1 15