Summary
Summary Basic probability
- Course
- Institution
organised with a nice layout
[Show more]
Seller
Follow
ambermcluckie
Content preview
STATSCHAPTER 4
BASIC PROBABILITY
Probability principles:
- Probability distributions
- Mathematical expectation
- Binomial and Poisson distributions
Sample space:
- All possible outcomes of a variable
Events:
Simple event:
- Described by single characteristic
Joint event:
- Described by 2 or more characteristics
Complement of an event A (denoted A’):
- All events that are not part of event A
Probability:
- The numerical value representing the chance, likelihood, or possibility that a certain event
will occur
- Between 0 and 1
Impossible event:
- An event that has no chance of occurring
- Probability = 0
Certain event:
- An event that is sure to occur
- Probability = 1
Mutually Exclusive Events:
- Events that cannot occur simultaneously
- A or B – never both
Collectively Exhaustive Event:
- One of the events must occur
- The set of events covers the entire sample space
- The entire sample space is “exhausted”
Visualizing Probability:
- Venn Diagram:
o A∪B
A or B
o A∩B
A and B
, Approaches to Assessing the Probability of Events:
A Priori:
- Based on prior knowledge
X number of ways ∈which theevent occurs
- Probability of occurrence = =
T total number of possible outcomes
- Assuming all outcomes are equally likely
Empirical Probability:
- Based on observed data
X number of ways ∈which theevent occurs
- Probability of occurrence = =
T total number of possible outcomes
- Assuming all outcomes are equally likely
Subjective Probability:
- Based on combination of an individual’s past experience, personal opinion and analysis of a
situation.
- Differs from person-to-person
Simple Probability:
- Probability of a simple event
number of outcomes satisfying A
- P (A) =
total number of outcomes
Joint Probability:
- Probability of an occurrence of 2 or more events (joint event)
number of outcomes satisfying A∧B
- P (A and B) =
totalnumber of outcomes
Marginal Probability:
- P (A) = P (A and B1) + P (A and B2) + … + P (A and Bk)
- Where B1, B2, …, Bk are k mutually exclusive and collectively exhaustive events.
Marginal & Joint Probabilities in Contingency Table:
Event Event Total
B1 B2
A1 P (A1 and B1) P (A1 and B2) P (A1)
A2 P (A2 and B1) P (A2 and B2) P (A2)
Total P (B1) P (B2) 1
Joint Probabilities Marginal (Simple) Probabilities
Probability Summary:
- P is the numerical measure of the likelihood that an event will occur.
- P of any event must be between 0 and 1, inclusively.
0 P (A) 1 for any event A
- The sum of the probabilities of all mutually exclusive and collectively exhaustive events is 1
P(A) + P(B) + P(C) = 1
If A, B, and C are mutually exclusive and
collectively exhaustive
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller ambermcluckie. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $2.83. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
67232 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now