{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

03.stats-review2-2rv

# 03.stats-review2-2rv - Lecture 3 Review of Statistics(Part...

This preview shows pages 1–6. Sign up to view the full content.

Lecture 3:  Review of Statistics (Part 2) Two Random Variables BUEC 333  Summer 2009 Simon Woodcock

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

View Full Document
Two Random Variables Most interesting questions in economics involve 2 (or more) variables what’s the relationship between education and earnings? what’s the relationship between stock price and profits? We describe the probabilistic relationship between two (or more) random variables using three kinds of probability distributions: the joint distribution marginal distributions conditional distributions
The Joint Distribution The joint distribution of discrete RVs X and Y is the probability that the two RVs simultaneously take on certain values, say x and y . That is, Pr( X = x , Y = y ) Example: the relationship between weather and commuting time. Let C denote commuting time. Suppose commuting time can be long ( C = 1) or short ( C = 0). Let W denote weather. Suppose weather can be fair ( W = 1) or foul ( W = 0). There are four possible outcomes: ( C = 0, W = 0), ( C = 0, W = 1), ( C = 1, W = 0), ( C = 1, W = 1). The probabilities of each of these outcomes define the joint distribution of C and W : Foul Weather (W=0) Fair Weather (W=1) Total Short Commute (C=0) 0.15 0.25 0.4 Long Commute (C=1) 0.55 0.05 0.6 Total 0.7 0.3 1

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

View Full Document
Marginal Distributions When X,Y have a joint distribution, we use the term marginal distribution to describe the probability distribution of X or Y alone. We can compute the marginal distribution of X from the joint distribution of X,Y by adding up the probabilities of all possible outcomes where X takes a particular value. That is, if Y takes one of k possible values: Example: commuting time and weather. The marginal distribution of weather is in blue. The marginal distribution of commuting time is in yellow. ( 29 = = = = = k i i y Y x X x X 1 , Pr ) Pr( Foul Weather (W=0) Fair Weather (W=1) Total Short Commute (C=0) 0.15 0.25 0.4 Long Commute (C=1) 0.55 0.05 0.6 Total 0.7 0.3 1
Conditional Distributions The distribution of a random variable Y conditional on another random variable X taking a specific value is called the conditional distribution of Y given X . The conditional probability that Y takes value y when X takes value x is written Pr( Y = y | X = x ).

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 16

03.stats-review2-2rv - Lecture 3 Review of Statistics(Part...

This preview shows document pages 1 - 6. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online