Chapter 5 Probability Distributions (Discrete Variables)

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MTH 160 Statistics I Brigitte Martineau Chapter 5 Mean and Variance of Discrete Probability Distribution Goal: To describe the ________________ and the _______________________ of a population Let’s review first! 1. The mean of a sample is represented by ___________. 2. s 2 and s are the ____________ and _____________ ____________ of the _________. 3. s 2 , and s are called ____________ _________________. 4. µ (lowercase Greek letter “mu”) is the _______________ of the _________________ 5. 2 (“sigma squared”) is the ______________ of the________________. 6. σ (lowercase Greek letter “sigma”) is the _____________ _________________ of the _________________ ___. 2 7. µ, σ and are called _______________ ________________. 2 (A parameter is a constant. µ, σ and are typically unknown values.) The Mean of a Discrete Random Variable The mean, µ, of a discrete random variable x is found by ____________________ each possible value of x by its own probability and then adding all the _________________ together. xP( x) Notes: The mean is not necessarily a value of the random variable The mean ________ is a population parameter that is usually unknown. We would like to ____________________ its value. The Variance of a Discrete Random Variable Page 6 of 14
MTH 160 Statistics I Brigitte Martineau Chapter 5 2 The variance, , of a discrete random variable x is found by _________________ each possible value of the squared deviation from the mean, 2 ( x ) , by its own probability and then _____________ all the products together. 2 x 2 x P x 2 P( x) ( ) xP( x) 2 2 x P( x) 2 The Standard Deviation of a Discrete Random Variable 2 Examples: Find the mean, the variance and the standard deviation of the following probability x distribution: P( x) for x 1 and 2 3 Page 7 of 14
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Chapter 5 Probability Distributions (Discrete Variables)

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