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Unit 5 Section 4.1 4.1: Probability Distributions Variables – a characteristic or attribute that can assume different variables. Within this unit, since we are discussing probability, the variables are called random variables. Random Variable – is a variable whose values are determined by chance. Variables can also be discrete (have a finite number of values or an infinite number of countable values) or continuous (can assume all values between any two given intervals. Section 4.1 Discrete Probability Distribution – lists each possible value the random variable can assume, together with its probability. The probabilities are determined theoretically or by observation. The probability of each value must be between 0 and 1. The sum of all the probabilities in the distribution must sum to 1. Section 4.1 Example 1: Construct a probability distribution for rolling a single die. Step 1: Determine the sample space Step 2: Determine the probability for each outcome. Step 3: Construct the probability distribution. Section 4.1 Example 2: Represent graphically the probability distribution for getting heads when tossing three coins. Step 1: Determine the sample space Step 2: Determine the probability for each outcome. Step 3: Construct the probability distribution. Step 4: Construct your graph Section 4.1 Things to remember… Outcomes will be listed on your x-axis. Probabilities will be listed on your y-axis. You do not have to start your outcomes with 0 or on the origin. Your probabilities will sum to 1. Each probability must be between 0 and 1. Section 4.1 Example 3: During the summer months, a rental agency keeps track of the number of chainsaws it rents each day during a period of 90 days. The number of saws rented per day is represented by the variable X. The results are shown below: X # of Days 0 45 1 30 2 15 Total: 90 Compute the probability P(X) for each X, and construct a probability distribution and graph for the data. Section 4.1 a) b) c) d) Example 4: Determine if each distribution is a probability distribution. If not, state why. X 0 5 10 15 20 P(x) 1/5 1/5 1/5 1/5 1/5 X 1 2 3 4 P(x) 1/4 1/8 1/16 9/16 X 0 2 4 6 P(x) -1.0 1.5 0.3 0.2 X 2 3 7 P(x) 0.5 0.3 0.4 Section 4.1 Homework: Pg. 197 – 198 (9 - 27 ODD)