Chapter 4 Discrete Probability Distributions 4.1 Probability Distributions I.Random Variables A random variable x represents a numerical value associated5with each outcome of a probability experiment.

There are two types of random variables Discrete random variables have a finite or countable number of possible outcomes that can be listed. (Whole numbers) Continuous random variables have an uncountable number of outcomes, represented by an interval on the number line. (Decimals and fractions) Example & TIY #1 (p173)

II. Discrete Probability Distributions A discrete probability distribution lists each possible value that a random variable can assume, together with its probability. And must satisfy… – 0 ≤ P(x) ≤ 1 – ∑ P(x) = 1

Because probabilities represent relative frequencies we can use a relative frequency histogram to display our data. Constructing a Discrete Probability Distribution 1.Make a frequency distribution for the possible outcomes. 2.Find the sum of the frequencies. 3.Find the probability of each possible outcome by dividing its frequency by the sum of the frequencies. 4.Check that each probability is between 0 and 1 and the sum is 1.

Examples Example 2 (p174) TIY#2

More Examples Example 3 (p175) TIY #3 Example 4 (p175) TIY#4

HW: p # 8-26 even & #28 (a) ONLY

4.1 continues… III.Mean, Variance & Standard Deviation Mean: µ = ∑ x ∙ P(x) – Represents theoretical average and sometimes is not a possible outcome. – Round 1 decimal place further than your data. (Finish #28 from hw as example)

Standard Deviation – Variance: σ 2 = ∑ (x - µ) 2 ∙ P(x) – St. Dev. : σ = √ σ 2

IV.Expected Value Same formula as the mean E(x) = ∑ x ∙ P(x) E(x) = 0 means it’s a fair game or the break even point HW: p #30-38even