advertisement

Name: _______________________ Class: __________ Date:_____________ Math SL: 23B Discrete Probability Distributions Review: 1. The diagram shows a circle of radius π cm. Find the perimeter and area of the shaded region. 1 radian 2. Let f (x) = 4 - x , x 4 and g (x) = x2, x (a) Find (g ◦ f ) (2); (b) Find f −1(x); . (c) Write down the domain of f −1. 1 23B Discrete Probability Distributions Today’s Objectives: (1) to understand discrete probability distributions Discrete Probability Distributions A probability distribution for a discrete random variable is a list of each possible value of the random variable and the probability that each value occurs. The probability that the variable X takes value x is written as P(X = x) or sometimes just P(x) . Probability distributions can be given as a table, graph, or sometimes even a function P(x). Example 1: Let X be the random variable that represents the sum when two dice are tossed. Tabulate the probability distribution for X. The probability pi of any given outcome lies between 0 and 1, i.e. 0 £ pi £ 1. n If there are n possible outcomes then åp i = ______ . i =1 Or in other words: p1 + p2 + p3 + .... + pn = ____. Example 2: Find k for the following probability distributions: (a) x 0 1 2 P(x) 0.3 k 0.5 (b) P(x) = k (x + 2) for x = 1, 2, 3. 2 Example 3: A bag contains 5 blue and 3 green tickets. Two tickets are randomly selected without replacement. We let X denote the number of blue tickets selected. (a) Find the probability distribution of X. (b) Suppose instead that three tickets are randomly selected without replacement. Find the probability distribution of X for X = 0, 1, 2, 3. Hmwk#51 23B Discrete probability distributions Pg. 633 # 1(b), 3(b), 4, 5, 6(b), 8, 11 Note: I would strongly recommend that you start to review for the next test. If you have any questions regarding topics/concepts, be proactive and seek help. If you feel you need more practice, then be proactive and COMPLETE more problems. Continue researching a math exploration topic – find math involved. 3