Introductory Biostatistics

births). If we apply the national IMR to the New England states, we would
have

y¼ð 11 : 9 Þð 164 : 2 Þ

F1954 infant deaths

Then the event of having as few as 1585 infant deaths would occur with a
probability

Prðda 1585 Þ¼Pr za

1585
1954

ffiffiffiffiffiffiffiffiffiffi

1954

p



¼Prðza
 8 : 35 Þ

F 0

The conclusion is clear: Either we observed an extremely improbable event, or
infant mortality in the New England states is lower than the national average.
The rate observed for the New England states was 9.7 deaths per 1000 live
births.

3.5 BRIEF NOTES ON THE FUNDAMENTALS

In this section we provide some brief notes on the foundation of some methods
in previous sections. Readers, especially beginners, may decide to skip it with-
out loss of continuity.

3.5.1 Mean and Variance

As seen in Sections 3.3 and 3.4, a probability density functionf is defined so
that:

(a) fðkÞ¼PrðX¼kÞin the discrete case

(b) fðxÞdx¼PrðxaXaxþdxÞin the continuous case

For a continuous distribution, such as the normal distribution, the meanm
and variances^2 are calculated from:

(a) m¼

Ð

xfðxÞdx

(b)s^2 ¼

Ð

ðx
mÞ^2 fðxÞdx

For a discrete distribution, such as the binomial distribution or Poisson dis-
tribution, the meanmand variances^2 are calculated from:

BRIEF NOTES ON THE FUNDAMENTALS 137