Consider the toss of a single weighted coin. Suppose a 0 is recorder if the result is tails and a 1 is recorded if the result is heads. If we let p denote the probability that the coin lands on heads, then (1-p) is the probability that it will land
Onceagain,considerthetossingofafair6sided die,andletAbetheeventanevennumberis observed. 3 Number of outcomes in A Then P(A) = =
6
Total number of outcomes
Thisdefinitionofprobabilitywillworkaslongas thesamplespaceisfinite. Tousethisdefinition,itisimportan
Once again, consider the tossing of a fair 6sided die, and let A be the event an even number is observed. 3 Number of outcomes in A Then P(A) = =
6
Total number of outcomes
This definition of probability will work as long as the sample space is
To begin this section, we will be looking at
unemployment data from 1989. This will
lead us naturally into Conditional
Probability.
Education
Employed
Total
5,299
Unemploy
ed
406
Elementary School
High School, 1-3 years
8,144
705
8,149
High School, 4 ye
MATH 1780: Introduction to Probability
Instructor: Jason Snyder
Contents
Section 1: Random Variables and Their Probability Distributions Section 2: Expected Values of Random Variables Section 3: The Bernoulli Distribution Section 4: The Binomi
Consider a game in which you toss two coins, if the two coins match then you win $1; if they do not match you lose $1. In the long run, how much would you expect to win or lose? Solution: Since the chances of winning equal the chances of losing, on
Suppose we want to determine a probability distribution that models the number of accidents that occur on I-635 in a given hour, or given week. We can think of the time interval as being broken into n sub-intervals such that P(one accident in a sub
As before, in the Binomial Distribution, we will be tossing a coin repeatedly. However this time, we will not be tossing it only n times. We are going to be tossing it an undetermined number of times. This time, we have an infinite sequence of
MATH 1780: Introduction to Probability
Instructor: Jason Snyder
Contents
Section 2: A Brief Review of Set Notation Section 3: Definition of Probability Section 4: Counting Rules Useful in Probability Section 5: Conditional Probability and Inde
The notion of probability requires three elements: A target population (either conceptual or real) from which observable outcomes are obtained Meaningful categorization of these outcomes A random mechanism for generating outcomes
Example 1: Imag
Homework Set 3: 1780
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