
308 Exposure-Response Modeling: Methods and Practical Implementation
A.4.1 Large sample properties and convergence
Here we only give basic concept and omit all technical details. When a series
random independent identical variables y
1
, ..., y
n
satisfy some technical con-
ditions, their mean ¯y
n
=
P
n
i=1
y
i
/n → E(y
i
). It is called the large number
theorem. Here ¯y
n
→ E(y
i
) means that when n increases to ∞, the difference
between ¯y
n
and E(y
i
) tends to zero, i.e., ¯y
n
converges to E(y
i
). However, since
¯y
n
is a random variable, we can only guarantee that the probability of the two
being different tends to zero. This statement has a number of versions math-
ematically ...