Chapter 7Chapter 7Continuous

Distributions

Notes page 137

Continuous random Continuous random variablesvariables

•Are numerical variables whose values fall within a range or interval

•Are measurements•Can be described by density curves

Density curvesDensity curves• Is always on or aboveon or above the

horizontal axis• Has an area exactly equal to oneequal to one

underneath it• Often describes an overall

distribution• Describe what proportionsproportions of the

observations fall within each range of values

Unusual density Unusual density curvescurves

•Can be any shape•Are generic continuous distributions

•Probabilities are calculated by finding the finding the area under the curvearea under the curve

1 2 3 4 5

.5

.25

P(X < 2) =

25.

225.2

How do you find the area of a triangle?

1 2 3 4 5

.5

.25

P(X = 2) =

0

P(X < 2) =

.25

What is the area of a line

segment?

In continuous distributions, P(P(XX < 2) & P( < 2) & P(XX << 2)2) are the same answer.

Hmmmm…

Is this different than

discrete distributions?

1 2 3 4 5

.5

.25

P(X > 3) =

P(1 < X < 3) =

Shape is a trapezoid –

How long are the bases?

2

21 hbbArea

.5(.375+.5)(1)=.4375

.5(.125+.375)(2) =.5

b2 = .375

b1 = .5

h = 1

Area of Trapezoid

2

21 hbbArea

The bases are always the 2 parallel sides.

1 2 3 4

0.25

0.50 P(X > 1) =.75

.5(2)(.25) = .25

(2)(.25) = .5

1 2 3 4

0.25

0.50P(0.5 < X < 1.5) =

.28125

.5(.25+.375)(.5) = .15625

(.5)(.25) = .125

Homework:

Page 140