183WI09PracticeMidterm2

183WI09PracticeMidterm2 - Math 183 Practice Midterm Exam II...

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Math 183 Practice Midterm Exam II 1. Define: (a) expected value of a random variable, discrete or continuous; p. 175 (b) variance of a random variable, discrete or continuous; p. 194 (c) standard deviation of a random variable; p. 195 (d) joint pdf of 2 random variables X and Y , discrete or continuous; p. 203, 206 (e) marginal pdfs, discrete or continuous; p. 205, 211 (f) independent random variables X and Y ; p. 216 (g) order statistics; p. 241 (h) likelihood function corresponding to a random sample from some distribution; p. 347 (i) maximum likelihood estimate for unknown parameter(s); p. 347 (j) method of moments estimate for unknown parameter(s); p. 357-358 (k) confidence interval for binomial parameter p ; p. 369 (l) unbiased estimator for unknown parameter; p. 381. 2. Complete the statement of the theorem: (a) If X is a discrete random variable with pdf p X ( k ) , then for any function g , E [ g ( X )] = ... p. 186. (b) If Y is a continuous random variable with pdf f Y ( y ) , then for any continuous function g , E [ g ( Y )] = ... p. 187. (c) For any random variable W and constants a and b , E [ aW + b ] = ... p. 187. (d) For any random variable W with mean μ = E [ W ] , E ± W 2 ² - μ 2 = ... p. 195. (e) For any random variable W and constants a and b , Var ( aW + b ) = ... p. 197. (f) Two random variables X and Y with joint pdf f X,Y ( x,y ) are independent if and only if . . . p. 216. (g) For two independent random variables X and Y , both discrete or both continuous, the pdf for their sum W = X + Y is . . . p. 220. (h) If X and Y are discrete random variables with joint pdf p X,Y ( x,y ) and g ( x,y ) is any function, then E [ g ( X,Y )] = ...
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183WI09PracticeMidterm2 - Math 183 Practice Midterm Exam II...

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