The Binomial Distribution

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Presentation transcript:

The Binomial Distribution 3.1c The Binomial Distribution The Mean and Variance of a Binomial Distribution X ~ B ( n , p ) The mean of the distribution is the expected value of X E(X) = np . The random variance of the distribution Var (X) = npq (q = 1 - p) The Standard Deviation √Var (X) = √(npq) (q = 1 - p)

c) the mean and variance of Y when Y = 3X + 4 Example X has a Binomial distribution where the number of trials are 30 and the probability of success is 0.4. Find the mean, the standard deviation, c) the mean and variance of Y when Y = 3X + 4 X ~ B ( 30 , 0.4 ) a) E(X) = np = 30 x 0.4 = 12 b) √Var (X) = √npq = √(30 x 0.4 x 0.6) = √7.2 = 2.68

Mathematics Statistics Unit S1 - WJEC X ~ B ( 30 , 0.4 ) c) E(Y) = E(3x + 4) = 3E(X) + 4 = 3 x 12 + 4 = 40 Var(Y) = Var(3x + 4) = 32 Var(X) = 9 x 7.2 = 64.8 Exercise 4.5c Mathematics Statistics Unit S1 - WJEC