To prove that if both a and b are even, then gcd(a, b) = 2gcd(a/2, b/2), let a and b be even integers. Then 2 is a common factor of both a and b, so 2 is a factor of gcd(a, b). Let 2c = gcd(a, b). Then a = n(2c) and b = m(2c) a/2 = nc and b/2 = mc so c 0 a/2 and c 0 b/2. Finish this proof by showing that c = gcd(a/2, b/2).

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...