Statistical Sciences 2244A/B Lecture Notes - Lecture 4: Institute For Operations Research And The Management Sciences
22 May 2018
School
Department
Professor
Stats 2244
Probability
Probability
- A measure of the long-run relative frequency of an event occurring, in identical repeated trials
- There are 2 ways to assign probabilities for outcomes:
- Classical approach:
o Make an assumption about the theoretical probabilities
o You don’t have to get up and do anything – you just think about the situation and make
an assumption about how likely a certain outcome is
o Ex: rolling a dice
▪ The possible outcomes are = {1,2,3,4,5,6}
▪ Each of those numbers is a simple event (cant be broken down further)
▪ X=rolling an even number (includes 2,4,6) →so x is an event that can be broken
down evne further into 2,4 or 6
o In order to come up with the probabilities, we assume that each of the outcomes is
equally likely to occur
- Relative frequency (frequentist) approximation:
o Proportion of times the outcome would occur in a long series of independent trials
Probability Model
- The 2 big components of a probability model is: list of outcomes and what are the probabilities
assigned to these outcomes
- Description of the outcomes and assigned probabilities for a random phenomenon
- Random outcomes are uncertain, but follow a regular distribution in a large # of repetitions
- In the context of sampling, random sampling means equal chance
- But in the context of probailiit, random does not mean equal, it means equal distribution
- Non-random = chaotic = doesn’t follow a regular distribution
Exploring Two-way tables & Probability
- Suppose the data from 2014-2015 was representative of typical annual enrolment
- )f we are randomly choosing a student, what is the probability that we select… (USE CHART
BELOW)
o A male or undergraduate student?
▪ P(Male or undergrad) = (1062+1474 – 645)/2199
▪ OR do it like this→( P(male) + P(undergrad) – P(male and undergrad))/total
o A graduate student, if we know she’s female?
find more resources at oneclass.com
find more resources at oneclass.com
Document Summary
A measure of the long-run relative frequency of an event occurring, in identical repeated trials. There are 2 ways to assign probabilities for outcomes: In order to come up with the probabilities, we assume that each of the outcomes is equally likely to occur. Relative frequency (frequentist) approximation: proportion of times the outcome would occur in a long series of independent trials. The 2 big components of a probability model is: list of outcomes and what are the probabilities assigned to these outcomes. Description of the outcomes and assigned probabilities for a random phenomenon. Random outcomes are uncertain, but follow a regular distribution in a large # of repetitions. But in the context of probailiit, random does not mean equal, it means equal distribution. In the context of sampling, random sampling means equal chance. Non-random = chaotic = doesn"t follow a regular distribution. Suppose the data from 2014-2015 was representative of typical annual enrolment.
