Chapter 7 Continuous Distributions Notes page 137

Continuous random variables Are numerical variables whose values fall within a range or interval Are measurements Can be described by density curves

Density curves on or aboveIs always on or above the horizontal axis equal to oneHas an area exactly equal to one underneath it Often describes an overall distribution proportionsDescribe what proportions of the observations fall within each range of values

Unusual density curves Can be any shape Are generic continuous distributions finding the area under the curveProbabilities are calculated by finding the area under the curve

P(X < 2) = How do you find the area of a triangle?

P(X = 2) =0 P(X < 2) =.25 What is the area of a line segment?

P(X < 2) & P(X < 2) In continuous distributions, P(X < 2) & P(X < 2) are the same answer. Hmmmm… Is this different than discrete distributions?

P(X > 3) = P(1 < X < 3) = Shape is a trapezoid – How long are the bases?.5( )(1)= ( )(2) =.5 b 2 =.375 b 1 =.5 h = 1

Area of Trapezoid The bases are always the 2 parallel sides.

P(X > 1) =.75.5(2)(.25) =.25 (2)(.25) =.5

P(0.5 < X < 1.5) = ( )(.5) = (.5)(.25) =.125

Homework: Page 140