Section4.3posted

Section4.3posted - STOR155,Section2 Tuesday,March16,2010...

Info iconThis preview shows pages 1–8. Sign up to view the full content.

View Full Document Right Arrow Icon
STOR 155, Section 2 Tuesday, March 16, 2010 Section 4.3
Background image of page 1

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

View Full DocumentRight Arrow Icon
4.3  Random variables Random variables  and  probability  distributions Discrete  random variables Continuous  random variables
Background image of page 2
4.3  Random variables The term  random variable   refers to a  numerical outcome of a random  phenomenon . Example A :  Toss a coin 3 times and let  X   be the number of heads.  X  is a random variable whose possible  values are 0, 1, 2, and 3. Example B :  Let  be a number chosen  using Excel’s =RAND() function. Y  is a random variable whose possible  values are the real numbers between 0 
Background image of page 3

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

View Full DocumentRight Arrow Icon
4.3  Random variables Any random variable has a set of  possible  values .  Subsets of that set are  events , and  probabilities   are assigned to the events.  (Just like a probability model, except that the sample  space must be a set of numbers.) This assignment is called the  probability  distribution   of the random variable. There are two kinds of random variable: discrete   random variable has a  finite  set of  possible values. continuous   random variable has a set of possible  values that is an  interval  of real numbers.
Background image of page 4
4.3  Random variables To specify the probability distribution of a  discrete   random variable, we list the  possible values along with the probability  assigned to each. Just like a finite sample space, except that with a  random variable, the outcomes are always  numbers. To specify the probability distribution of a  continuous   random variable, we give a  density curve  over the interval of possible  values. Then the probability of any event is the area  under the density curve, over the points in the 
Background image of page 5

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

View Full DocumentRight Arrow Icon
Example 1a  Choose a number at random from a table of  data that follows Benford’s Law.  Let  X  = first digit .   Then the possible values of  X  are 1,2,3,4,5,6,7,8,9, and the  probability distribution is (from Example 4.12, p. 248) Value of  X 1 2 3 4 5 6 7 8 9 Probability .301 .176 .125 .097 .079 .067 .058 .051 .046 A probability histogram of the distribution: 4.3  Random variables:  Discrete random variables
Background image of page 6
Example 1b :  Choose a digit from a table of random digits.  If 0, discard and draw again.  Let  be the digit chosen.   Then the possible values of  X  are 1,2,3,4,5,6,7,8,9, and the  probability distribution is (from Example 4.15, p. 248)
Background image of page 7

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

View Full DocumentRight Arrow Icon
Image of page 8
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 22

Section4.3posted - STOR155,Section2 Tuesday,March16,2010...

This preview shows document pages 1 - 8. Sign up to view the full document.

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