Show thatif A is similar to B, then a. det(A) = det(fi). The characteristic polynomial of A is the same as the characteristic polynomial of B. A is nonsingular if and only if B is nonsingular. If A is nonsingular, show that A -1 is similar to S -1 . A' is similar to B'.
10/26 The mean (expected value) of the probability distribution of a random variable x is The variance of the probability distribution of a random variable x is And the standard deviation is Player bets $1 on red in roulette. Let x = his net winnings. The Binomial Distributions An experiment has two outcomes, SUCCESS and FAILURE (we will count the SUCCESSES), Each time this experiment is performed, P(SUCCESS) = P, P(FAILURE) = 1- P = q. Do this n times and let x = # of SUCCESSES Arandom variable x is deﬁned ion this way is said to have a binomial distribution with parameters n and P. The possible values of x are 0,1,2,…..,n Notation: Whenever there are p and q m a stats problem, p+q = 1 q = 1 - P p + q = 1 p1 + q = 1 10/28