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Matleev Final Review

Matleev Final Review - Math351 Spring 2010 Final review...

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Math351 Spring 2010 Final review Warning: this is rather a review of the course than a review before the final exam. Consider it as a supplement to the excellent end-of-chapter reviews in the Ross’s book. This review consists of two parts: (1) A short list of basic notions (and only some facts). Make sure it is clear to you “what is what”. Typically, it is possible to define each of these notions in one clear sentence. 1 Try to do so. Only sometimes you will need to write a formula. (2) A collection of “naive” questions. Most questions can be answered very quickly, without any calculations or without long calculations. These questions are not, in general, a model for the final exam problems. Most questions do not contain traps; they do not seem easy, they are easy. 1. Basic notions Sample space Outcome Event Mutually disjoint events Probability of an event Independent events Conditional probability Reduced sample space “Conditioning” Bayes’s formula Random variable The indicator variable of an event Cumulative distribution function of a random variable Discrete random variable Continuous random variable Probability mass function of a discrete random variable The density function of a continuous random variable Expectation of a random variable (in the discrete case, and in the contin- uous case) Variance of a random variable Standard deviation of a random variable The hazard rate function (associated with a random variable) Joint cumulative distribution function of two random variables Joint probability mass function of two discrete random variables Jointly continuous random variables, joint density function Independent random variables Conditional probability mass function Conditional probability density function Change of variables in distributions and joint distributions Covariance of two random variables The correlation coefficient of two random variables Positively, negatively, zero correlated variables 1 Except for the most basic notions: sample space and probability
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Conditional expectation Moment generating function of a random variable Multiplication rule for moment generating functions of sums of independent random variables Uniqueness rule for moment generating functions Markov’s inequality Chebyshev’s inequality 2. Sample space, events, probabilities... (1) What is P { 2 + 2 = 5 } ?
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