Class notes
Intro to Probability Distribution
- Course
- PSYB07
- Institution
- University Of Toronto (U Of T )
An intro into probability distributions
[Show more]
Seller
Follow
Content preview
Probability
outline is on the side
Skewness and Kurtosis
➔two more descriptive stats, associated w/ spread
➔skewness:how symmetrical the observations are aroundthe mean
◆ important because it influences the measures of central tendency and probabilistic
distributions
◆ positive distribution/ left-skewed:the peak is towardsthe left and the tail is along the
right end of the curve
● extreme values are closer to the mean, meaning the mean is greater than the
median
● the mean is the better measure when looking at a positive distribution
◆ negative distribution/ right-skewed:the peak is towardsthe right and the tail is along the
left end of the curve
● extreme values are by the peak, meaning the mean is less that the median
● the median is the better measure ,when looking at a negative distribution
➔kurtosis:how clustered or flat the observations are
◆ mesokurtic:kurtosis of 0
● normal distribution
◆ leptokurtic:positive kurtosis
● skinner than usual
◆ platykurtic:negative kurtosis
● flatter than usual (think platypus w/ a flat beak)
◆ does not affect measures of central tendency
Probability Theory
➔provides description of hidden structure that exists within an infinite/large population of
observations/outcomes
◆ look at the structure within the chaos
➔way of defining boundaries between results of mere chance vs results not by mere chance
➔two approaches to probability
◆ rational
◆ empirical
, Approach Source Priority Starting Point
Rational (A priori) k nowledge based on r eason > experience; e xpected outcomes
reason/logic, not raises reasoning and (educated guess w/ all
experience logic to mathematical all information);
precision expected % are
determined before the
occurrence of an
outcome
Empirical (A k nowledge is based on experience > reason bserved outcome
o
posteriori) experience/observati (deduce based on
onrather than reason gathered info through
alone experience); expected
% determined on
experience; additional
observations could
lead to updating
current expectations
Basic Definitions
➔event/outcome:the occurrence of something that isobserved
➔probability:the likelihood of an event happening
◆ expressed in proportions (0-1) or percentages (0-100%)
◆ P(event) = number of event outcomes/total number of outcomes
➔complement rule:P(A) + P’(A) = 1OR100%
➔exampleofA priori/rational approach
◆ using a 6-sided die, what is the probability of rolling a 6?
● (possible outcomes: 1,2,3,4,5, and 6)
◆ P(6) = number of 6s on a die / total number of numbers on a die
● P(6) = 1 /6
● 0.1666667
➔exampleofA posteriori/empirical approach
◆ you have a bag of marbles. you don’t know how many red and black marbles are inside.
◆ Pick 1: you pick out a marble at random, it’s red. observed relative frequency between
red and black marbles?
● red = 100% and black = 0%
○ you haven’t witness a black marble from the bag yet to have any reason for
believing a black marble exists in the bag
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 sobikaaravi. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for CA$7.16. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
51292 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 15 years now