{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

lec4print - Continuous random variables Continuous...

Info icon This preview shows pages 1–12. Sign up to view the full content.

View Full Document Right Arrow Icon
Continuous random variables Continuous distributions Continuous random variables and probability distributions Artin Armagan Sta. 113 Chapter 4 of Devore January 28, 2009 Artin Armagan Continuous random variables and probability distributions
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Continuous random variables Continuous distributions Table of contents 1 Continuous random variables 2 Continuous distributions Uniform Normal Exponential Gamma Chi-squared Beta Artin Armagan Continuous random variables and probability distributions
Image of page 2
Continuous random variables Continuous distributions Mathematical definition Definition A random variable X is continuous if its set of possible values is an entire interval of real numbers: x [ A , B ] for A < B. Artin Armagan Continuous random variables and probability distributions
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Continuous random variables Continuous distributions Examples 1 Heights of people. 2 Amount of rainfall per square meter. 3 IQ scores. Artin Armagan Continuous random variables and probability distributions
Image of page 4
Continuous random variables Continuous distributions Probability distributions Definition Let X be a continuous rv. The probability density function (pdf) of X is a function p ( x ) such that for any two numbers a b IP ( a X b ) = integraldisplay b a p ( x ) dx . The probability that X takes values in the interval [ a , b ] is the area under the graph of the density function in the interval. Artin Armagan Continuous random variables and probability distributions
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Continuous random variables Continuous distributions Picture Artin Armagan Continuous random variables and probability distributions
Image of page 6
Continuous random variables Continuous distributions Restatement Proposition Let X be a continuous rv. Then for any number c, IP ( X = c ) = 0 and for any two numbers a < b IP ( a X b ) = IP ( a < X b ) = IP ( a X < b ) = IP ( a < X < b ) . Artin Armagan Continuous random variables and probability distributions
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Continuous random variables Continuous distributions Cumulative distribution function Definition The cumulative distribution function (cdf) F ( x ) for a continuous rv X is defined for every number x by F ( x ) = IP ( X x ) = integraldisplay x −∞ p ( u ) du . So for for each x, F ( x ) is the area under the density to the left of x. Artin Armagan Continuous random variables and probability distributions
Image of page 8
Continuous random variables Continuous distributions Picture -10 -8 -6 -4 -2 0 2 4 6 8 10 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 Artin Armagan Continuous random variables and probability distributions
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Continuous random variables Continuous distributions Matlab code x= -10:.01:10; y = normpdf(x,.5,1); plot(x,y,’r’); hold on; y1 = normcdf(x,.5,1); plot(x,y1,’b’); Artin Armagan Continuous random variables and probability distributions
Image of page 10
Continuous random variables Continuous distributions More properties Proposition Let X be a continuous rv with pdf p ( x ) and cdf F ( x ) . Then for any number a, IP ( X > a ) = 1 - F ( a ) , and for any two numbers a < b, IP ( a X b ) = F ( b ) - F ( a ) .
Image of page 11

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 12
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern