183WI09PracticeMidterm2

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

This preview shows pages 1–2. Sign up to view the full content.

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 )] = ...

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## This document was uploaded on 09/01/2011.

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online