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Statistics Notes: 6.1 Probability Distributions Do you remember? Create a relative frequency histogram. 6.1 Probability Distributions Random Variable: A numerical outcome of a random experiment. denoted X. Discrete Random Variable: A countable random variable Continuous Random Variable: A measurable random variable Examples: • The number of light bulbs in the school that burn out the next year. • The number of leaves on a randomly selected Oak tree. • The amount of time between calls to 911. Probability Distribution: A distribution of a random variable that gives the outcomes and their probabilities (relative frequencies). Probability Histogram A histogram that shows the relationship between the random variable (x) and its probability (y). Probability Distribution Probability Histogram Which of the following are probability distributions? Why? A. C. B. A Discrete Probability Distribution is: 1 Statistics Notes: 6.1 Probability Distributions The mean of a discrete random variable: I asked several students the ages of their cars and obtained the following data. 2, 4, 6, 6, 4, 4, 2, 3, 5, 5 Find the average age of the cars. 41 2 + 4 + 6 + 6 + 4 + 4 + 2 + 3 + 5 + 5 = = 4.1 10 10 The formula: = Mean of a Discrete Random Variable: Multiply the value of each random variable by its probability, then add up the products. Standard Deviation of a Discrete Random Variable: Suppose a basketball player historically makes 80% of her free throw attempts (free throws are independent). The table below gives the number of successful attempts in 3 shots and the probability of each outcome. the variance is .48 2 Statistics Notes: 6.1 Probability Distributions Expected Value: A term life insurance policy will pay a beneficiary a sum of money upon the death of the policy holder. These policies have premiums that must be paid annually. Suppose a life insurance company sells a $250,000 one year term life insurance policy to a 20yearold male for $350. The probability he will survive the year is 0.99865. Compute the expected value of this policy to the insurance company. Expected Value: This is the mean of the discrete random variable. Suppose the same life insurance company sells a $250,000 one year term life insurance policy to a 49yearold female for $520. The probability she will survive the year is 0.99791. Compute the expected value of this policy to the insurance company. HW: p335 #1 11 odds, 15, 19, 21, 23 3