Lesson10S1.pptx

# Lesson10S1.pptx - TAIBAH UNIVERSITY Faculty of...

• 42

This preview shows pages 1–13. Sign up to view the full content.

TAIBAH UNIVERSITY Faculty of Science Department of Math . ةبيط ةعماج مولعلا ةيلك تايضايرلا مسق Probability and Statistics for Engineers STAT 305 Teacher : Dr.Moustapha Abdellahi First Semester 1438/1439

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

Random Variables and Probability Distributions Lesson 10
Concept of Random Variable Contents Discrete Probability Distribution and Cumulative Distribution Function Continuous Probability Distribution and Cumulative Distribution Function

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

In a statistical experiment, it is often very important to allocate numerical values to the outcomes. Experiment : testing two components. ( D =defective, N =non-defective) Sample space : S ={DD,DN,ND,NN} Concept of Random Variable Example
Let X = number of defective components when two components are tested. Assigned numerical values to the outcomes are: Concept of Random Variable Sample point (Outcome) Assigned Numerical Value (x) DD 2 DN 1 ND 1 NN 0 Notice that, the set of all possible values of the random variable X is {0, 1, 2}.

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

A random variable X is a function that associates each element in the sample space with a real number (i.e., X : S R.) " X “ ( capital letter ) denotes the random variable . " x " ( small letter ) denotes a value of the random variable X . Concept of Random Variable Definition : Notation
Two balls are drawn in succession without replacement from an urn containing 4 red balls and 3 black balls. The possible outcomes and the values y of the random variable: Y , where Y is the number of red balls, are Example :

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

Let X be the random variable defined by the: waiting time, in hours, between successive speeders spotted by a radar unit. The random variable X takes on all values x for which x > 0 . Example :
A random variable X is called a discrete random variable if its set of possible values is countable, i.e., x { x 1 , x 2 , …, x n } or x { x 1 , x 2 , …} In most practical problems: A discrete random variable represents count Types of Random Variable Discrete Random Variable :

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

A random variable X is called a continuous random variable if it can take values on a continuous scale, i.e., x {x: a < x < b; a, b R} In most practical problems: A continuous random variable Types of Random Variable Continuous Random Variable:
A discrete random variable X assumes each of its values with a certain probability. Example: Experiment : tossing a non- balance coin 2 times independently. H= head , T=tail Sample space: S ={HH, HT, TH, Probability Distributions (Discrete ) Discrete Probability Distributions

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

Sample point (Outcome) Probability Value of X (x) HH P(HH)=P(H) P(H)=1/3 1/3 = 1/9 2 HT P(HT)=P(H) P(T)=1/3 2/3 = 2/9 1 TH P(TH)=P(T) P(H)=2/3 1/3 = 2/9 1 TT P(TT)=P(T) P(T)=2/3 2/3 = 4/9 0 Probability Distributions (Discrete ) Suppose P(H) = ½P(T) P(H)= 1/3 and P(T)= 2/3 Let X = number of heads
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern