# Econometrics: Statistics Homework - Marginal distributions

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*timer*Asked: Feb 8th, 2019

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**Tags:**statistics Econometrics Unemployment Rate joint probability distribution employment status marginal distributions

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Homework 1

SW Chapter 2

1. The following table gives the joint probability distribution between employment status and

college graduation among those either employed or looking for work in the working age

US population for 2008.

Unemployed

Employed

(Y = 0)

(Y = 1)

Total

Non-college grads (X = 0)

0.037

0.622

0.659

College (X = 1)

0.009

0.332

0.341

Total

0.046

0.954

1

a) Using the definition of the expected value, show that the expected value of a binary random

variable equals probability of the outcome 1. In other words, suppose you have a random

variable that takes on either a value of 1 (called "outcome 1" in the problem set) with probability

p or a value of 0 with probability (1-p)). The question asks you to show, using the formula for

expected value which you learned in class, that the expected value of this variable equals p

E(x) = ∑𝑛𝑖=1 𝑋𝑖 ∗ 𝑝(𝑋𝑖)

E(x) = 0*(1-p) + 1* p

E(x) = 0 + p

E(x) = p

b) What are the marginal distributions of X and Y? Using a) compute E(Y) and E(X).

E(y) = p (Y...

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