Formula for final exam Biostatistics
n
Px 
n!
(n  X)!
n
Cx 
Dr Alia Al nuaimat
n!
X!(n  X)!
Discrete Variables
 Expected Value (or mean)=   E(X) 
N
 x P( X  x )
i 1
 Variance of a discrete variable = σ 2 
i
N
 [x
i 1
i
i
 E(X)]2 P(X  x i )
----------------------------------------------------------------------------------------------------------------------
Binomial Probability Distribution
P(X  x | n , p) 
x
n!
p (1  p) n  x
x!(n  x)!
σ 2  np(1 - p )
μ  np
-------------------------------------------------------------------------------------------------------------------------
Poisson Distribution
P( X  x |  ) 
e   x
x!
μλ
σ2  λ
x = number of events in an area of opportunity,
 = expected number of events, e = base of the natural logarithm system (2.71828...)
-----------------------------------------------------------------------------------------------
Normal Distribution
Z
X μ
σ
X  μ  Zσ
---------------------------------------------------------------------------------------------------
Central Limit Theorem (or CLT)
Standard error of mean = 𝝈
Confidence Interval for a Mean
√𝒏
/
√
or
/
√
Formula for final exam Biostatistics
Error Margin
SE
=
Sample Size
𝛼/2
𝑛=
𝜎
𝑛
or
2
2
𝛼/2
/
Dr Alia Al nuaimat
√
2
Hypothesis Testing
ZSTAT 
Xμ
σ
n
t STAT 
X μ
S
n
z
α = tail area
central area = 1 – 2α
0.10
0.80
z
0.05
0.90
z
0.025
0.95
z
0.01
0.98
z
0.005
0.99
z
.10
.05
α
= 1.28
= 1.645
.025
.01
.005
= 1.96
= 2.33
= 2.58