ch8 - Ch 8 RandomVariablesand DiscreteProbability...

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

View Full Document Right Arrow Icon
1 Ch  Random Variables and  Discrete Probability  Distributions random variable  is a  function  or rule that assigns a  number  to each outcome of an experiment. Instead of talking about the coin flipping event as  {heads, tails}, we can think of it as {1, 0}. Or, a numerical event, which we can call  the number  of heads when flipping a coin
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 We can have two types of random variables: Discrete  Random Variable (these take on a  countable   number of values like values on the roll of dice: 2, 3, …,  12) Continuous  Random Variable (these take on values that  are  uncountable , like time (30.1 minutes? 30.10001  minutes? or…) useful analogy  is “Integers are Discrete, while Real  Numbers are Continuous” Probability distributions  are a listing of all possible  outcomes of an experiment and the corresponding  probability. – A  discrete  distribution is based on random variables which  can assume only clearly separated values. – A  continuous     distribution can assume an infinite number  of values within a given range.
Background image of page 2
3 Discrete Prob. Distribution Consider a random experiment in which a coin is tossed  three times.  Let  X  be the number of heads.  Let H  represent the outcome of a head and T the outcome of a  tail. Possi bl e Coi n Toss Number of Resul t s 1st 2nd 3r d Heads 1 T T T 0 2 T T H 1 3 T H T 1 4 T H H 2 5 H T T 1 6 H T H 2 7 H H T 2 8 H H H 3
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 Probability distribution of  the number of heads in 3  tosses Number of Pr obabi l i t y of Heads, X out come, P( X) 0 1/ 8 = 0. 125 1 3/ 8 = 0. 375 2 3/ 8 = 0. 375 3 1/ 8 = 0. 125 Tot al 1 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 1 2 3 Probability
Background image of page 4
5 The  mean  is the long-run average value of the random  variable, and is also referred to as its  expected  value , E(X), in a probability distribution. )] ( [ X p X × Σ = μ The  variance  measures the amount of spread (variation)  of a distribution. )] ( ) [( 2 2 X p X X - Σ = σ
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 Example Find the  mean , variance, and standard deviation for the  population of the number of color televisions per  household = 0(.012) + 1(.319) + 2(.374) + 3(.191) + 4(.076) + 5(.028) = 2.084
Background image of page 6
7 Find the mean,  variance , and standard deviation for the  population of the number of color televisions per  household. = (0 – 2.084) 2 (.012) + (1 – 2.084) 2 (.319)+…+(5 – 2.084) 2 (.028) = 1.107
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 Find the mean, variance, and  standard deviation  for  the population of the number of color televisions per  household.
Background image of page 8
9 Laws of Expected Value E(c) = c E(X + c) = E(X) + c E(c X ) = cE( X ) Laws of  Variance V(c) = 0 V(X + c) = V(X) V(cX) = c 2 V(X) Laws of Expected Value and Variance
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.

Page1 / 43

ch8 - Ch 8 RandomVariablesand DiscreteProbability...

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