Advanced High-School Mathematics

350 CHAPTER 6 Inferential Statistics

6

1

t

y y=fx(t) =2t

Two important observations are in order.

(a) For any observationxofX, 0≤x≤1.

(b)

∫ 1

0 f(x)dx= 1

(See Exercise 1, below.)

We see that the above density curve has quite a bit of “skew” to it;
in particular it’s clear that a random measurement ofXis much more
likely to produce a value greater than .5 than less than .5.

6.2.1 The normal distribution

Thenormal density functionhas the general form

f(x) =

1

√

2 πσ

e−

(^12) (x−σμ)^2
whereμandσare constants, orparameters^13 of the distribution. The
graph is indicated below forμ= 1 andσ= 2:
(^13) We’ll have much more to say about parameters of a distribution. In fact, much of our statistical
study will revolve around the parameters.