4.2: Probability Models
Exercise 4.29:
Exercise 4.30:
Ex 3: Suppose two people are randomly selected from the world
population. Let E be the event that both of these people live in
Europe. Which of the following events is Ec ?
(a) The event that neither o
MAT 221 - Fall 2016
Formulae
If X is a discrete random variable taking on values x1 , . . . , xk with respective probabilities
p1 , . . . , pk , then the mean is X = x1 p1 + + xk pk , the variance is
q
2
2 .
X
= (x1 X )2 p1 + + (xk X )2 pk , and the stan
4.4: Means and Variances of Random Variables
Mean of a Continuous Random Variable
Recall: The probability distribution of continuous random variables
is described by a density curve.
The mean lies at the center of symmetric density curves such
as the norm
4.5: General Probability Rules
Recall: Events A and B are independent if they have no influence
on each others occurrence.
If A and B are independent, then P(A and B) = P(A)P(B).
If A and B are independent, then P(B|A) = P(B).
Example: Supposed two dice a
4.5: General Probability Rules
Conditional Probability
Notation: P(A|B) = the probability of A given that event B has
occurred.
P(A|B) =
number of outcomes in A and B
number of outcomes in B
Example 1: Consider the current U.S. Senate membership:
Female
M
Chapter 4: Probability The Study of Randomness
4.1: Randomness
4.2: Probability Models
4.3: Random Variables
4.4: Means and Variances of Random Variables
4.5: General Probability Rules
4.5: General Probability Rules
Objectives
Venn diagrams
General additi
4.3: Random Variables
How do we assign probabilities to events involving a continuous
random variable X ?
Example: Let X be the amount of time (in minutes) that you will
have to wait for a friend who will be at most 15 minutes late.
Then, X is a continuou
4.4: Means and Variances of Random Variables
Example 2: Compare the means of the random variables X and Y :
X
Probability
2
0.4
3
0.6
Y = 2X
Probability
4
0.4
6
0.6
4.4: Means and Variances of Random Variables
Example 3: Linda is a sales associate at an a
Chapter 4: Probability The Study of Randomness
4.1: Randomness
4.2: Probability Models
4.3: Random Variables
4.4: Means and Variances of Random Variables
4.5: General Probability Rules
4.1: Randomness
A phenomenon is random if individual outcomes are
unce