General Information
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The exam will be held on Tuesday, March 20, from 5:30pm to 7:00pm, in Smith Labs 154.
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Plan to arrive a few minutes early to allow time to distribute the exams.
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The exam will cover material from sections 3.4, 3.5, 3.6, 3.7, 3.8, 3.9, 3.10, and 3.11 in the text.
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Cell-phones should be turned OFF for the duration of the exam.
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You may use a non-graphing, scientific calculator during the exam. No other calculator or electronic device may be used during the exam.
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This is a closed-book exam. No books or notes may be used during the exam.
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You will be expected to show all of your work. A correct answer with insufficient justification
may not receive full credit.
Topics
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Binomial Distribution. Be able to determine if a random variable has a binomial distribution. Know and be able to apply the formulas for the distribution function, mean, and variance of a binomial random variable. Also be able to use the distribution function to perform derivations like those in the proof of Theorem 3.7 and Exercise 3.55. Table 1 in Appendix 3 (or a portion of it) will be provided, so be sure you know how to use it to calculate probabilities involving binomial random variables.
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Geometric Distribution. Be able to determine if a random variable has a geometric distribution. Know and be able to apply the formulas for the distribution function, mean, and variance of a geometric random variable.
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Negative Binomial Distribution. Be able to determine if a random variable has a negative binomial distribution. Know and be able to apply the formulas for the distribution function, mean, and variance of a negative binomial random variable.
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Hypergeometric Distribution. Be able to determine if a random variable has a hypergeometric distribution. Know and be able to apply the formulas for the distribution function, mean, and variance of a hypergeometric random variable.
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Poisson Distribution. Be able to determine if a random variable has a Poisson distribution. Know and be able to apply the formulas for the distribution function, mean, and variance of a Poisson random variable. Also be able to use the distribution function to perform derivations like those in the proof of Theorem 3.11 and Exercise 3.138. Table 3 in Appendix 3 (or a portion of it) will be provided, so be sure you know how to use it to calculate probabilities involving Poisson random variables.
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Moment Generating Functions. Know the definition of a moment generating function of a random variable. Be able to calculate the moment generating function of a given random variable, and how to use a moment generating function to find the moments of a random variable.
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Probability Generating Functions. Know the definition of a probability generating function of a random variable. Be able to calculate the probability generating function of a given random variable, and how to use a probability generating function to find the probability distribution of a random variable, as well as the factorial moments of a random variable.
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Tchebysheff's Theorem. Know and be able to use Tchebysheff's theorem to estimate probabilities of a random variable with known mean and standard deviation.
Preparing for the Exam
Here are a some exercises from the text to use for practice. Solutions to most of the odd-numbered exercises are in the back of the text.
Chapter 3
Exercises 184, 186, 187, 188, 192, 193, 195, 196, 197, 199, 200, 201, 202, 203, 204, 205, 206, 207, 208, 209, 211, 213, 214
