Econ 2810 Problem Set 1 | Solution

Econ 2810 Intro to Statistics and Computing In Economics Spring 2016
Problem Set 1

1. A survey of introductory statistics students showed that 29.7% have Verizon wireless service, 73.4%
have a Visa credit card, and 20.3 % have both. What is the probability that a student uses Verizon or
has a Visa credit card?
2. Based on actual data, the probability that a customer at a certain Noodles & Company restaurant will
order a dessert with the meal is 0.08. The probability that a customer will order a bottle beverage is
0.14. The joint probability that a customer will order both a dessert and a bottled beverage is 0.0112.
Is ordering a dessert independent of ordering a bottle beverage? Why or why not?
3. Consider the following table:
Table 1.1: Smoking and Gender for Individuals Age 65
Gender Never Smoked (N) Former Smoker (R) Current Smoker (S) Total
Male (M) 3,160 5,087 2,320
Female (F) 10,437 2,007 15,305
Total 13,597 7,948 4,327 25,872
a. Given that a 65 year old individual is a smoker, what is the probability that person is male?
4. Consider two random variables, X and Y , which are both discrete and can take on values 1 or 2. The
probabilities for (X\ Y ) are given in the table below:
Y = 1 Y = 2
X = 1 1
4
1
8
X = 2 3
8
1
4
a. Find E(Y 2);E(X2)
b. Find 2X
; 2Y
c. Find P(X = 1jY = 1), P(X = 2jY = 2)
1