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Y Dosraniad Binomial
The Binomial Distribution
Cymedr ac amrywiant Dosraniad Binomial
The Mean and Variance of a Binomial Distribution
X~B(n,p)
Cymedr yr hapnewidyn yw gwerth disgwyliedig X.
The mean of the distribution is the expected value of X.
E(X) = np
Amrywiant yr hapnewidyn X
The random variance of the distribution
Var (X) = npq
(q = 1 - p)
Y Gwyriad Safonol
The Standard Deviation
√Var (X) = √(npq)
(q = 1 - p)
Enghraifft - Example
Mae gan X ddosraniad Binomial lle mae’r nifer yn 30 a’r
tebygolrwydd o lwyddiant yn 0.4.
X has a Binomial distribution where the number of trials are 30 and
the probability of success is 0.4.
Darganfyddwch Find
a) y cymedr, the mean,
b) y gwyriad safonol, the standard deviation,
c) cymedr ac amrywiant Y pan mae Y = 3X + 4
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
Ymarfer/Exercise 4.5c
Mathemateg - Ystadegaeth Uned S1 – CBAC
Mathematics Statistics Unit S1 - WJEC