EconRandomVariables

EconRandomVariables - Introductory Statistics Stats 210...

Info iconThis preview shows pages 1–13. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Introductory Statistics Stats 210 Random Variables
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 What are Random Variables? A random variable is a variable whose value is a NUMERICAL outcome of a random phenomenon The sample space consists of elements that are not necessarily numerical The probability function assigns probabilities to elements of the sample space Random variables can numerically represent any element from the sample space
Background image of page 2
3 What are Random Variables? Example: Draw a person from the population Either male or female Define Random Variable X=1 if female and X=0 if male We denote a random variable with a capital letter and a realization of the random variable with a small letter
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
4 What are Random Variables? We can define a RV in any way Example: 3 coin tosses RV: X 1 = outcome RV: X 2 = number of heads
Background image of page 4
5 Discrete vs. Continuous RVs Discrete RVs = has a finite number of possible values = can only take on (discrete) set of values Continuous RVs = can take on ALL VALUES in an interval of numbers
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
6 Discrete Random Variables Binary Gender (male, female) College Graduate (yes=1/no=0) Usually coded 0/1 Multiple Values Marital Status (Multiple Values: Single, Married, Divorced, Separated)
Background image of page 6
7 Continuous Random Variables Examples Height Weight Wages 10k time Education
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
8 Probability Distribution of a RV Remember: The probability function p(x) provided us with probabilities of outcomes and events It can do just the same for a Random Variable We distinguish between probability distributions for discrete and continuous RVs
Background image of page 8
9 Probability Distribution: Discrete RV The probability distribution of a discrete random variable X list the values of X and their respective probabilities The probability distribution has to satisfy two requirements Every probability p i much be between 0 and 1 p 1 + p 2 + p 3 + …. + p k =1 Value of X x 1 x 2 …x k Probability p 1 p 2 ... p k
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
10 Probability Distribution: Discrete RV Example: Number of Heads in 3 coin tosses Let’s look at a graph = = = = = otherwise 0 3 X if 2 X if 1 X if 0 X if ) ( 8 1 8 3 8 3 8 1 x f
Background image of page 10
11 Probability Distribution: Graph 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0 1 2 3
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
12 Probability Distribution: Continuous RV Remember: A continuous RV can take ANY value in an INTERVAL of numbers Let’s say the interval is between 0 and 3 Pick a number between 0 and 3 Let’s take 2.9 Can we find a number between 2.9 and 3? Let’s take 2.99 Can we find a number between 2.99 and 3?
Background image of page 12
Image of page 13
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 48

EconRandomVariables - Introductory Statistics Stats 210...

This preview shows document pages 1 - 13. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online