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. 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

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. 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

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

Discrete Probability Distribution Table Value of X: x1 x2 x3 … xn Probability: p1 p2 p3 pn AP Statistics, Section 7.1, Part 1

Probability Distribution Table: Number of Heads Flipping 4 Coins TTTT TTTH TTHT THTT HTTT TTHH THTH HTTH HTHT THHTHHTT THHH HTHH HHTH HHHT HHHH X 1 2 3 4 P(X) 1/16 4/16 6/16 AP Statistics, Section 7.1, Part 1

Discrete Probability Distributions Can also be shown using a histogram AP Statistics, Section 7.1, Part 1

AP Statistics, Section 7.1, Part 1

What is the average number of heads? AP Statistics, Section 7.1, Part 1

AP Statistics, Section 7.1, Part 1

Continuous Random Variable A continuous random variable X takes all values in an interval of numbers. AP Statistics, Section 7.1, Part 1

Distribution of Continuous Random Variable AP Statistics, Section 7.1, Part 1

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

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

AP Statistics, Section 7.1, Part 1 Assignment Exercises: 7.1 - 7.11 AP Statistics, Section 7.1, Part 1