Chapter 7 Continuous Distributions Notes page 137.
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Transcript of Chapter 7 Continuous Distributions Notes page 137.
![Page 1: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/1.jpg)
Chapter 7Chapter 7Continuous
Distributions
Notes page 137
![Page 2: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/2.jpg)
Continuous random Continuous random variablesvariables
•Are numerical variables whose values fall within a range or interval
•Are measurements•Can be described by density curves
![Page 3: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/3.jpg)
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
![Page 4: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/4.jpg)
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
![Page 5: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/5.jpg)
1 2 3 4 5
.5
.25
P(X < 2) =
25.
225.2
How do you find the area of a triangle?
![Page 6: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/6.jpg)
1 2 3 4 5
.5
.25
P(X = 2) =
0
P(X < 2) =
.25
What is the area of a line
segment?
![Page 7: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/7.jpg)
In continuous distributions, P(P(XX < 2) & P( < 2) & P(XX << 2)2) are the same answer.
Hmmmm…
Is this different than
discrete distributions?
![Page 8: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/8.jpg)
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
![Page 9: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/9.jpg)
Area of Trapezoid
2
21 hbbArea
The bases are always the 2 parallel sides.
![Page 10: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/10.jpg)
1 2 3 4
0.25
0.50 P(X > 1) =.75
.5(2)(.25) = .25
(2)(.25) = .5
![Page 11: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/11.jpg)
1 2 3 4
0.25
0.50P(0.5 < X < 1.5) =
.28125
.5(.25+.375)(.5) = .15625
(.5)(.25) = .125
![Page 12: Chapter 7 Continuous Distributions Notes page 137.](https://reader036.fdocuments.us/reader036/viewer/2022062309/56649f4a5503460f94c6c27b/html5/thumbnails/12.jpg)
Homework:
Page 140