Chapter 4 Sections 4'1 4'3

1
Chapter 4 Sections 4.1 - 4.3

• Discrete Random Variables

2
Random Variable

• A random variable is a variable that assumes
  numerical values associated with the random
  outcomes of an experiment, where one and only one
  numerical value is assigned to each sample point.

3
Two Types of Random Variables

• Discrete Random variable can assume a countable
  number of values.
• Continuous random variable can assume any of the
  points contained in one or more intervals. The
  number of points that can be assumed are infinite.

4
Probability Distributions for Discrete Random
Variables

• A probability distribution for a discrete random
  variable is a table, formula, or graph that
  assigns a probability to each value that the
  random variable can assume.

5
For Example

• For a family of three children let x be the
  number of boys and p(x) is the probability of
  obtaining that number of boys.
• Options
• BBB,BBG,BGB,BGG
• GBB,GBG,GGB,GGG

6
Requirements for the Probability Distribution of
Discrete Random Variables

• P(x)0 for all values of x
• Sp(x) 1
• ( the sum of all the probabilities must add up
  to One)

7
Expected Values of Discrete Random Variables

• Expected value is another name for mean. It is
  also called expectation.
• The symbols for expected value are
• E(x)Exp µ
• Expected value is calculated according to the
  formula E(x)µSxp(x)

8
Variance and Standard Deviation of Discrete
Random Variables

• Var(x)s²E(x²) - µ²
• STD(x) s the square root of the variance

9
Chebyshevs Rule for Discrete Random Variables

• P(µ-1sltxlt µ1s) 0
• P(µ-2sltxlt µ2s) 75
• P(µ-3sltxlt µ3s) 89
• Note Chebyshevs Rule applies to any probability
  distribution.

10
Empirical Rule for Discrete Random Variables

• If the probability distribution for a discrete
  random variable is mound shaped and symmetric,
  then
• P(µ-1sltxlt µ1s) 68
• P(µ-2sltxlt µ2s) 95
• P(µ-3sltxlt µ3s) 100

11
Homework Sections 4.1 4.3

• Page 177, 4.3, 4.4, 4.5
• Pages 179-181, 4.6, 4.7, 4.8,4.17,4.18,4.19
• Pages 186 -188, 4.22,4.23,4.28,4.29,4.30,4.31