stat3021-ch3-Sol.pdf

stat3021-ch3-Sol.pdf - STAT 3021 Chapter 3 Random variables...

Info icon This preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon
STAT 3021 Chapter 3. Random variables and probability distributions 3.1 Concept of a random variable In an experiment that can have more than one possible outcome, we use random variable to describe outcomes numerically. For example, when we flip a fair coin three times, all possible outcome may be written S = { HHH, HHT, HTH, THH, HTT, THT, TTH, TTT } where T = tail, H= head. Let X be the random variable that represents the number of heads. Then X = 0 , 1 , 2 , or 3 . Outcome x P ( X = x ) P ( X x ) TTT x = 0 P ( X = 0) = 1 8 P ( X x ) = 1 8 TTH, HTT, THT 1 3 8 4 8 HHT, HTH, THH 2 3 8 7 8 HHH 3 1 8 1 Definition 3.1 Note: We denote a random variable by a capital letter , such as X . We denote values of variables by lower case letters, such as x or x 1 . Notation P ( X = x ) represents the probability that random variable X is equal to a particular value x . For instance, P ( X = 1) refers the probability that a random variable X is equal to 1. Example 1. (Example 3.3 in page 82) Consider the simple condition in which components are arriving from the product line and they are stipulated to be defective or not defective. Define the random variable X by X = ( 1 , if the component is defective , 0 , if the component is not defective . 1
Image of page 1

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

View Full Document Right Arrow Icon
STAT 3021 As in Example 1 if there are only 2 categories for a variable and you are interested in one category, Bernoulli random variable , X , takes 1 for the category of interest and 0 for the other category. 2
Image of page 2
STAT 3021 Definition 3.2 A random variable is called a discrete random variable if its set of possible outcome is countable. A Bernoulli random variable is the simplest discrete random variable.
Image of page 3

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

View Full Document Right Arrow Icon
Image of page 4
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