In Exercises 21 and 22, mark each statement True or False. Justify each answer.

a. If d is a real number and f is a nonzero linear functional defined on Rn, then [f : d] is a hyperplane in Rn.

b. Given any vector n and any real number d, the set

{x: nx = d} is a hyperplane.

c. If A and B are nonempty disjoint sets such that A is compact and B is closed, then there exists a hyperplane that strictly separates A and B.

d. If there exists a hyperplane H such that H does not strictly separate two sets A and B, then

(conv A) (conv B)

Lecture 1 Nicole Rubenstein August 28, 2017 1 Overview & Introduction Probability Concepts (STAT 3375): ▯ Chapter 2: Basic Probability ▯ Chapter 3: Discrete Probability Distributions ▯ Chapter 4: Continuous Probability Distributions ▯ Chapter 5: Multivariate Probability Distributions ▯ Chapter 6: Transformations of Random Variables...