MAT204_Lecture_04.pptx

MAT204_Lecture_04.pptx - FACULTY OF INFORMATION TECHNOLOGY...

Info icon This preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Ta Quang Hung, Ph.D. FACULTY OF INFORMATION TECHNOLOGY Probability & Statistics Spring, 2017 Lecture 4: Random Variables & Distributions – Part 2
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
Lecture 4 Probability & Statistics Contents Page 2 2 Bivariate Distributions 4 Conditional Distributions 3 Marginal Distributions 5 Summary 1 Cumulative Distributions
Image of page 2
Lecture 4 Probability & Statistics 1. Definition & Properties of Cumulative Distribution Functions 2. c.d.f. of a Discrete & Continuous Distributions 3. Quantile Function Page 3 CUMULATIVE 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
Lecture 4 Probability & Statistics Definition of Cumulative Distribution Function The cumulative distribution function (c.d.f.) of a random variable is the function this function it can be used for both discrete and continuous random variables. It should be emphasized that the cumulative distribution function is defined as above for every random variable , regardless of whether the distribution of is discrete, continuous, or mixed. Page 4
Image of page 4
Lecture 4 Probability & Statistics Example for c.d.f. of Discrete Variable Example 1: Machine breakdown Page 5 The probability mass function can be used to construct the cumulative distribution function as follows: Notice that the cumulative distribution function is a step function that starts at a value of 0 for small values of and increases to a value of 1 for large values of . The steps occur at the points and which are the possible values of the cost, and the sizes of the steps at these points and are simply the values of the probability mass function .
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
Lecture 4 Probability & Statistics Example for c.d.f. of Discrete Variable Example 2: Binomial distribution Page 6 The p.d.f. of Binomial distribution The c.d.f. of Binomial distribution
Image of page 6
Lecture 4 Probability & Statistics Example for c.d.f. of Continuous Variable Example 3: Metal Cylinder Production Suppose that the diameter of a mental cylinder has a probability density function Page 7 The probability density function for metal cylinder diameter This is a valid probability density function because The cumulative distribution function of the metal cylinder diameters can be constructed from the probability density function as
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
Lecture 4 Probability & Statistics Example for c.d.f. of Continuous Variable Page 8 The c.d.f. is an increasing function between the limits and with ,
Image of page 8
Lecture 4 Probability & Statistics Example for c.d.f. of Continuous Variable Example 4: Normal distribution Page 9 The p.d.f. of Normal distribution The c.d.f. of Normal distribution
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
Lecture 4 Probability & Statistics
Image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.
  • Spring '18
  • Probability distribution, Probability theory, probability density function, New South Wales, Cumulative distribution function

{[ 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