MCS 341 Problem Assignments

5. Multivariate Probability Distributions

Sections to read	Topics	Suggested problems	Assigned problems	Due Date
5.1 5.2	Introduction Joint probability distributions	5.1, 5.7	5.4, 5.6, 5.12	F 11/12
5.3	Marginal and conditional probability distributions	5.17, 5.23, worksheet	5.20 (Also do (b) given Y₁ = 1.), 5.22, 5.28	M 11/15
5.3	Extra credit	Fix handout; if X,Y have joint density f(x,y) = kxy²[x>0,y>0,x+y<4], then P(1<X<2, 1<Y<3) = ?		M 11/15
5.4	Independent random variables	5.39, 5.51, 5.53	5.42, 5.44, 5.50, 5.54	W 11/17
5.5 5.6	The expected value of a function of random variables Special theorems	5.63, 5.69	5.64, 5.65, 5.72	F 11/19
5.7	The covariance of two random variables	5.77, 5.82, 5.84	5.76, 5.78	M 11/22
5.7	Extra credit	(1) Show that our correlation coefficient reduces to the sample correlation r if P((X,Y) =(x_j,y_j)) = 1/n for j = 1, ..., n. (2) (#5.137) Show that -1 < correlation coefficient < 1.
5.8	The expected value and variance of linear functions of random variables	Examples 5.27, 5.29	5.87, 5.90
5.9	The multinomial probability distribution	5.99, 5.103, 5.104
5.10	The bivariate normal distribution (optional)	5.108, 5.109
5.11	Conditional expectations	In-class examples
Class notes	Sum of a random number of r.v.s	Extra credit (ps) (pdf)		F 12/3

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