Download Y Dosraniad Binomial

The Binomial Distribution
The Mean and Variance of a Binomial Distribution
X~B(n,p)
The mean of the distribution is the expected value
. X
of
E(X) = np
The random variance of the distribution
Var (X) = npq
The Standard Deviation
√Var (X) = √(npq)
(q = 1 - p)
(q = 1 - p)
Example
X has a Binomial distribution where the number of trials are 30 and
the probability of success is 0.4.
Find
a) the mean,
b) 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
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