find the solution of the differential equation that satisfies the given boundary condition(s). y 7y 12y 0, y102 y112 1x

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 A2 outcome experiment with P(success) = p and P(Failure) = q = 1 - p) is performed n times and x is the number of timed success happens. Such an x has a binary probability distribution with parameters n and p. The possible values of x are 0,1,….,n. Binomial n = 5 P(success) = P What’s P(2) P(SSFFF) = p^3, q^2 P(FFFSS) = p^3, q^2 1.)Any way of getting 2 successes has probability p^3, q^2 = p^3, q^2. 2.) There are5C2 = 10 ways to get 2 successes. 1.) SSFFF 2.) SFSFF 3.) SFFSF 4.) SFFFS 5.) FSSFF 6.) FSFSF 7.) FSFFS 8.) FFSSF 9.) FFSFS 10.) FFFSS ____ ____ ____ ____ ____ 1st 2nd 3rd 4th 5th 5C2 = 10 3.) What’s P(4) Any way of getting 4 successes has probability p^4, q^1 And there are 5C 4= 5 ways Prob: p.p.p.p.q 1.) 2.) 3.) 4.) If x is a bi