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 4.2, 4.3, 4.4, 4.5, 4.6, 4.7, 4.9, 4.10, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.8, and 5.9 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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Continuous Random Variables. Know how to use the cdf and pdf of a continuous random variable to calculate probabilities, expected value, variance, and quantiles.
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Sepcific Distributions. Know the pdf, mean and variance or the following distributions: uniform, normal, gamma, beta.
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Moment Generating Functions. Know the definition of the moment generating function of a random variable and how it is used to find the moments.
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Joint Densities and Distributions. Know how to use a joint pdf for a pair of random variables to calculate probabilities, expected values, variances, marginal pdfs and conditional pdfs.
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Independence. Know how to determine if a pair of random variables is independent, using their joint pdf, joint cdf, or in terms of the conditional and marginal pdfs.
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Covariance. Know the definition of the covariance of two random variables. Know that independent random variables have zero covariance, but not vice versa. Know what the correlation coefficient tells us about how the random variables are related. Know how covariance is used in calculating the variance of a linear combination of random variables.
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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 4
Exercises 160, 161, 162, 164, 165, 167, 168, 169, 174, 176, 184
Chapter 5
Exercises 145, 146, 147, 148, 149, 150, 151, 152, 153, 158
