PSYC 202 Chapter Notes - Chapter 5: Sample Space, Random Variable, Normal Distribution
15 Jun 2018
School
Department
Course
Professor
Random trial
- Any process with multiple outcomes but whose result on a particular trial cannot be
predicted
o E.g. drawing a ball on bingo
Sample space:
- The space of all possible outcomes
o E.g. list of all balls
Event:
- Any subset of the sample space
- A specific outcome.
- Either happens or doesn’t happen
o E.g. when trying to find B11, B11 is our event
e.g. when rolling a die, looking at the occurrence of getting a 1. The sample space is all possible
outcomes S ={1,2,3,4,5,6} - shows the list of outcomes. Random trial is rolling a die. Event
‘A’ for a ‘1’: A = {1}
Probability
- The frequency of an events occurrence
- Law of Large Numbers
- E.g. die – P(A)= 1/6
Random variable
- Variable with a random outcome
- Outcome can be a sample space for a random trial or a function of this
- E.g. die – random variable is any number rolled
- E.g rolling two dice
o Random trial = rolling two dice
o Sample space = any combinations
o Random variable = sum of numbers rolled X={2,3,4…10,11,12}
o Event A for sum of 5: A= {(1,4), (2,3), (3,2), (4,1)}
o Probability of A: P(A)=4/36
Distribution of random variables
- Describes the probability of each outcome of a random variable
- Includes all possible outcomes for that variable
- The area always sums to one
- The entire distribution is summarizing the Law of Large Numbers
Document Summary
Any process with multiple outcomes but whose result on a particular trial cannot be predicted: e. g. drawing a ball on bingo. The space of all possible outcomes: e. g. list of all balls. Either happens or doesn"t happen: e. g. when trying to find b11, b11 is our event e. g. when rolling a die, looking at the occurrence of getting a 1. The sample space is all possible outcomes s ={1,2,3,4,5,6} - shows the list of outcomes. Outcome can be a sample space for a random trial or a function of this. E. g. die random variable is any number rolled. Describes the probability of each outcome of a random variable. The entire distribution is summarizing the law of large numbers. Addition rule: if two events are mutually exclusive, then the probability of one or the other is their sum, p(a or b) = p(a)+p(b)
