Chapter 18 Random Variables750
f 20 .k/
0:18
0:16
0:14
0:12
0:10
0:08
0:06
0:04
0:02
0
k
0 5 10 15 20
Figure 18.4 The pdf for the unbiased binomial distribution fornD 20 ,f 20 .k/.
23 headsplus... the probability of flipping no heads.
The General Binomial Distribution
If the coins are biased so that each coin is heads with probabilityp, then the
number of heads has ageneral binomial density functionspecified by the pdf
fn;pWŒ0::nç!Œ0;1çwhere
fn;p.k/D
n
k
!
pk.1 p/n k: (18.1)
for somen 2 NCandp 2 Œ0;1ç. This is because there are