Post on 17-Jan-2016
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