22. Let G be a group. Prove that G is abelian if and only if (ab) -1 = a-1b-1 for all a,b G.
Hypothesis 1: G is a group. G is abelian.
Hypothesis 2: G is a group. (ab)-1 = a-1b-1 for all a,b G.
Conclusion 1: (ab)-1 = a-1b-1 for all a,b G.
Conclusion 2: G
(16 pts.) Multiple Choice. For eachproblem,circle the singlebestresponse. 1. If X and Yare randomvariablesanda,b,c areconstants, then E(aX + bY + c)
= a E(X)
+ b E(Y) + c
,
(~:;!~r~' b. Sometimes
c. Never
2. If X and Yare independent randomvariab
(W! m) Saumw
1. (57 pts.) This problem concerns making $1 bets on the so-called 2-spot game in
Classic Keno at video lottery machines in Rapid City. You, as a gambler, get to choose
from 2 numbers (or spots) from 1-80; the video lottery machine then choo
(BLUE) §0LJWN§
1. (57 pts.) This problem concerns making $1 bets on the so-called 2spot game in
Classic Keno at most video lottery machines in the Four Aces Casino in Deadwood.
You, as a gambler, get to choose from 2 numbers (or spots) from 1-80; the vid
Abstract
In this paper we will investigate the general Stochastic process. In addition to the Stochastic process, we
will also be investigating a specific Stochastic process referred to as the Levy process. The Levy process,
named for the French mathemati