Ch07 - Chapter 7 Random Variables and Discrete probability...

Info iconThis preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
  1 Random Variables and Discrete probability Distributions Chapter 7
Background image of page 1

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

View Full DocumentRight Arrow Icon
  2 7.2 Random Variables and Probability Distributions A random variable is a function or rule that assigns a numerical value to each simple event in a sample space. A random variable reflects the aspect of a random experiment that is of interest for us. There are two types of random variables: Discrete random variable Continuous random variable.
Background image of page 2
  3 A random variable is discrete if it can assume a countable number of values. A random variable is continuous if it can assume an uncountable number of values. 0 1 1/2 1/4 1/16 Continuous random variable After the first value is defined the second value, and any value thereafter are known. Therefore, the number of values is countable After the first value is defined, any number can be the next one Discrete random variable Therefore, the number of values is uncountable 0 1 2 3 . .. Discrete and Continuous Random Variables
Background image of page 3

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

View Full DocumentRight Arrow Icon
  4 A table, formula, or graph that lists all possible values a discrete random variable can assume, together with associated probabilities, is called a discrete probability distribution . To calculate the probability that the random variable X assumes the value x, P( X = x), add the probabilities of all the simple events for which X is equal to x, or Use probability calculation tools (tree diagram), Apply probability definitions Discrete Probability Distribution
Background image of page 4
  5 If a random variable can assume values x i , then the following must be true: 1 ) x ( p . 2 x all for 1 ) p(x 0 . 1 i x all i i i = Requirements for a Discrete Distribution
Background image of page 5

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

View Full DocumentRight Arrow Icon
  6 Distribution and Relative Frequencies In practice, often probability distributions are estimated from relative frequencies. Example 7.1 A survey reveals the following frequencies (1,000s) for the number of color TVs per household. Number of TVs Number of Households x p(x) 0 1,218 0 1218/Total = .012 1 32,379 1 .319 2 37,961 2 .374 3 19,387 3 .191 4 7,714 4 .076 5 2,842 5 .028 Total 101,501 1.000
Background image of page 6
  7 Determining Probability of Events The probability distribution can be used to calculate the probability of different events Example 7.1 – continued Calculate the probability of the following events: P(The number of color TVs is 3) = P(X=3) =.191 P(The number of color TVs is two or more)
Background image of page 7

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

View Full DocumentRight Arrow Icon
  8 Probability calculation techniques can be used to develop probability distributions Example 7.2 A mutual fund sales person knows that there is 20% chance of closing a sale on each call she makes. What is the probability distribution of the number of sales if she plans to call three customers? Developing a Probability Distribution
Background image of page 8
  9 Solution Use probability rules and trees Define event S = {A sale is made}. Developing a Probability Distribution P(S)=.2 P(S C )=.8 P(S)=.2 P(S)=.2 P(S)=.2 P(S)=.2 P(S C )=.8 P(S C )=.8 P(S C )=.8 P(S C )=.8 S S S S S S C S S S S S S C S S S S S S C S S S S S S C P(S)=.2 P(S C )=.8 P(S C )=.8 P(S)=.2 P(x) .2 3 = .008 3(.032)=.096 3(.128)=.384 .8 3 = .512 (.2)(.2)(.8)= .032 Probability Distribution Finding Probability/ Probability Distribution
Background image of page 9

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

View Full DocumentRight Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 06/06/2011 for the course ADMS 2320 taught by Professor Rochon during the Spring '08 term at York University.

Page1 / 48

Ch07 - Chapter 7 Random Variables and Discrete probability...

This preview shows document pages 1 - 10. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online