×

### Let's log you in.

or

Don't have a StudySoup account? Create one here!

×

or

## ECON 300

by: Patricia Soto

557

14

4

# ECON 300 ECON 300

Patricia Soto
UIC
GPA 3.89

Enter your email below and we will instantly email you these Notes for Econometrics

(Limited time offer)

Unlock FREE Class Notes

Everyone needs better class notes. Enter your email and we will send you notes for this class for free.

Week 1 Notes
COURSE
Econometrics
PROF.
Irina Horoi
TYPE
Class Notes
PAGES
4
WORDS
CONCEPTS
Econometrics, ECON 300
KARMA
Free

## Popular in Economcs

This 4 page Class Notes was uploaded by Patricia Soto on Monday January 18, 2016. The Class Notes belongs to ECON 300 at University of Illinois at Chicago taught by Irina Horoi in Winter 2016. Since its upload, it has received 557 views. For similar materials see Econometrics in Economcs at University of Illinois at Chicago.

×

## Reviews for ECON 300

×

×

### What is Karma?

#### You can buy or earn more Karma at anytime and redeem it for class notes, study guides, flashcards, and more!

Date Created: 01/18/16
ECON  300   Week  1  Notes   Random Variable (RV) – A variable whose value is determined by a stochastic process. • Denoted by a capital letter like X. • The value that a random valuable takes on is denoted by a lower case letter like x. • 2 Kinds of RV o Discrete RV – Takes on finite number of values § Ex. The # of successful foul shots made out of 2 attempts = X It can take on any value in the set {0,1,2} § Discrete RV is characterized by its probability density function (PDF) (*Think of PDF as distribution) ú PDF- f(X-subj) = p-subj for subj = 1, 2 ……k ú Here there three possible value of RV X and the jth value occurance is given by p; The pdf free throws makde out of 2 attempts ú All values add to 1 o Continuous RV – Takes on infinite possibilities. Takes on any specific real value with 0 probability. § Ex. Consider the RV age and for simplicity suppose people are evenly distributed between age 0 and 100 years. Let’s measure age in hours instead of years. {0,..100* 365*24 – 876,000} = .00001 (probability of picking any age) § The precision of your measurement dictates how many possible values an RV can take on in reality. § In the real world everything is discrete however, when the # od outcomes with non-zero probability of occurring becomes large you can treat is as continuous. § Continuous RV can be described by a cumulative density function (CDF) ú F(x) = P( X ≤ x) => this funcation takes x + returns the probability that the RV takes on a value less than or equal to x. ú Properties of CDF (Consider constants a, b, c.) • P(x >c) = 1-F(c) • P( a<X≤b) = F(b) – F(a) • P(x≥c) = P(>c) -> useful for hypothesis testing ECON  300   Week  1  Notes   o Multiple RVs- when we are concerned with more than one RV we use a joint pdf => f-subx,suby (x,y) = P(x=x, y=y) => This is the probability. o Independence – RVs X and Y are independent if and only if f-subx,suby(x,y) = f-subx(x) * f-suby(y) § f-subx(x) & f-suby(y) are known as marginal probability functions § Just the pdf of own RV that are evaluated at x and y ú Ex: 2 RVs • L: {1,0) (1 = late, 0 = on time) • R: {1,0} (1 = raining, 0 = not raining) Late Not late Raining .10 .10 Not Raining .08 .72 • Are raining and late independent of each other? o Add rows across and down o Late Not Late Raining .10 .10 .20 Not .08 .72 .80 Raining ú .18 .82 ú P-subx*suby = .1 ú .2 ≠ .18 ≠ .36 o Conditional Distribution – The probability of something happening conditional on something else (tells us the probability of x conditional on Y = y § P (Y = y, X = x) = f-suby|subx (y1) = f- subx,suby(x,y)/ f-subx(x) ú | = conditional X = years of schooling Y = income in thousands 30 40 50 F(x) 9 .2 .1 .1 .4 ECON  300   Week  1  Notes   12 .05 .2 .05 .3 16 .1 .00 .2 .3 F(y) .35 .30 .35 P(Y=y|X=x) = f-subysubk = f(x,y)/f(x) = P(Y = 40| X= 12) = .2/.3 = 2/3 *marginal probability = add horizontally E[X] = xsub1 * psub1 + xsub2* psub2 + …..xsubn * psubn Ex. Rolling Dice • E[Roll] = 1/6[ 1+2+3+4+5+6] E[Y] = 30*.035 + 40*.03 +50*.05 =40 Properties of Expectations E[c] = c (distribution = 1 at whatever the value is) E[aX + b] = E[aX] + E[b] (E[b] = b (because of first property)) =aE[x] +b E[X +Y] = E[X] + E[Y] Median – What is the middle value of the distribution, used for non- symmetrical distributions (i.e very skewed) • Formal definition: The middle value. A random draw from the distribution will have an equal value of being above the median as being below the median. F(x-subm) = .5 F = cdf x-subm =median Right tailed distribution : median > mean Conditional Expectations – Just like expectations but with given values E[Y|X=x] =Σ y-sub0 * f-suby|x(y-sub0|x) Properties of Conidtional Expectations 1. E[x(x)|X] = c(x) 2. E[a(x)*Y +b(x)|X] = a(x)E[Y|X] + b(x) 3. If X and Y are independent, E [Y|X] = E[Y] 4. The Law of Iterated Expectations • E-suby[E[Y|X]] =E[Y] Variances Var(x) = E[(x-µ)^2] = E[x^2] - µ^2 = σ^2 Properties of Variance 1. Var(c) = o 2. Var(aX +c) = Var(aX + Var(b) = a^2Var(X) If X and Y are independent: 3. Var(X+Y) = Var(X) + Var(Y) ECON  300   Week  1  Notes   4. Var(Y-X) = Var(X) + Var(Y) Standard Deviation – Variance^2 Covariance – measure of how two RV move with each other Cor(X,Y) = E[(X-µsubx)(Y-µsuby)]= σsubxsuby Properties 1. Cov(X,Y) =0 if X,Y are independent 2. Cov(aX +b, cY+d) = a*c*Cov(X,Y) 3. |Cov(X,Y)| ≤ sd(X) *sd(Y) Correlation – measure of linear strength Corr(X,Y) = Cov(X,Y)/sd(x)*sd(Y) (varies from -1 to 1)

×

×

### BOOM! Enjoy Your Free Notes!

×

Looks like you've already subscribed to StudySoup, you won't need to purchase another subscription to get this material. To access this material simply click 'View Full Document'

## Why people love StudySoup

Jim McGreen Ohio University

#### "Knowing I can count on the Elite Notetaker in my class allows me to focus on what the professor is saying instead of just scribbling notes the whole time and falling behind."

Jennifer McGill UCSF Med School

#### "Selling my MCAT study guides and notes has been a great source of side revenue while I'm in school. Some months I'm making over \$500! Plus, it makes me happy knowing that I'm helping future med students with their MCAT."

Steve Martinelli UC Los Angeles

Forbes

#### "Their 'Elite Notetakers' are making over \$1,200/month in sales by creating high quality content that helps their classmates in a time of need."

Become an Elite Notetaker and start selling your notes online!
×

### Refund Policy

#### STUDYSOUP CANCELLATION POLICY

All subscriptions to StudySoup are paid in full at the time of subscribing. To change your credit card information or to cancel your subscription, go to "Edit Settings". All credit card information will be available there. If you should decide to cancel your subscription, it will continue to be valid until the next payment period, as all payments for the current period were made in advance. For special circumstances, please email support@studysoup.com

#### STUDYSOUP REFUND POLICY

StudySoup has more than 1 million course-specific study resources to help students study smarter. If you’re having trouble finding what you’re looking for, our customer support team can help you find what you need! Feel free to contact them here: support@studysoup.com

Recurring Subscriptions: If you have canceled your recurring subscription on the day of renewal and have not downloaded any documents, you may request a refund by submitting an email to support@studysoup.com