Introductory Biostatistics

The model is concerned with the total number of successes inntrials as a
random variable, denoted byX. Its probability density function is given by

PrðX¼xÞ¼

n

x



pxð 1 
pÞn
x forx¼ 0 ; 1 ; 2 ;...;n

where

n

x



is the number of combinations ofxobjects selected from a set ofn

TABLE 3.11

Outcome

First
Patient

Second

Patient

Third

Patient

Fourth

Patient

Fifth

Patient Probability

Number of

Patients having

Side E¤ects

SSSSSð 0 : 1 Þ^5! 5
SSSSNð 0 : 1 Þ^4 ð 0 : 9 Þ! 4
SSSNSð 0 : 1 Þ^4 ð 0 : 9 Þ! 4
SSSNNð 0 : 1 Þ^3 ð 0 : 9 Þ^23
SSNSSð 0 : 1 Þ^4 ð 0 : 9 Þ! 4
SSNSNð 0 : 1 Þ^3 ð 0 : 9 Þ^23
SSNNSð 0 : 1 Þ^3 ð 0 : 9 Þ^23
S S NNNð 0 : 1 Þ^2 ð 0 : 9 Þ^32
SNSSSð 0 : 1 Þ^4 ð 0 : 9 Þ! 4
SNSSNð 0 : 1 Þ^3 ð 0 : 9 Þ^23
SNSNSð 0 : 1 Þ^3 ð 0 : 9 Þ^23
SNSNNð 0 : 1 Þ^2 ð 0 : 9 Þ^32
SNNSSð 0 : 1 Þ^3 ð 0 : 9 Þ^23
SNNSNð 0 : 1 Þ^2 ð 0 : 9 Þ^32
SNNNSð 0 : 1 Þ^2 ð 0 : 9 Þ^32
S NNNNð 0 : 1 Þð 0 : 9 Þ^41
NSSSSð 0 : 1 Þ^4 ð 0 : 9 Þ! 4
NSSSNð 0 : 1 Þ^3 ð 0 : 9 Þ^23
NSSNSð 0 : 1 Þ^3 ð 0 : 9 Þ^23
NSSNNð 0 : 1 Þ^2 ð 0 : 9 Þ^32
NSNSSð 0 : 1 Þ^3 ð 0 : 9 Þ^23
NSNSNð 0 : 1 Þ^2 ð 0 : 9 Þ^32
NSNNSð 0 : 1 Þ^2 ð 0 : 9 Þ^32
N S NNNð 0 : 1 Þð 0 : 9 Þ^41
NNSSSð 0 : 1 Þ^3 ð 0 : 9 Þ^23
NNSSNð 0 : 1 Þ^2 ð 0 : 9 Þ^32
NNSNSð 0 : 1 Þ^2 ð 0 : 9 Þ^32
NNSNNð 0 : 1 Þð 0 : 9 Þ^41
NNNSSð 0 : 1 Þ^2 ð 0 : 9 Þ^32
NNNSNð 0 : 1 Þð 0 : 9 Þ^41
NNNNSð 0 : 1 Þð 0 : 9 Þ^41
N NNNNð 0 : 9 Þ^50

134 PROBABILITY AND PROBABILITY MODELS