STA 103: Lab 1
Solutions
1) tax ti paid by individual i is a function of income xi
ti = 0.1(xi 2000) i.e. at tax on all income over $2,000.
500 individuals, total income of $5,000,000
What is total tax revenue?
Total tax revenue is:
500
500
0.1(xi 2000)
t
Statistics 103, Lab 1:
Practice with n=1 notation
k
1
Linear properties of n n=1
k
Instructions: Hi Everyone. Here are the lab/discussion problems. The TAs will go over the
solutions in detail during lab/discussion (and hopefully have enough extra time to
Statistics 103: Midterm 1
Test Form D
(Dated: January 24, 2013)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until 11:50am to nish this test. You may use one sheet of notes and a
calcu
Statistics 103: Midterm 1
Test Form C
(Dated: January 24, 2013)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until 11:50am to nish this test. You may use one sheet of notes and a
calcu
Statistics 103: Midterm 3
Test Form B
(Dated: March 7, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until noon to nish this test. You may use one sheet of hand-written notes
and
Statistics 103: Midterm 2
Test Form A
(Dated: Feb 14, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until 11:50am to nish this test. You may use one sheet of hand-written
notes an
Statistics 103: Midterm 3
Test Form D
(Dated: March 7, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until noon to nish this test. You may use one sheet of hand-written notes
and
Statistics 103: Midterm 2
Test Form B
(Dated: Feb 14, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until 11:50am to nish this test. You may use one sheet of hand-written
notes an
Statistics 103: Midterm 2
Test Form C
(Dated: Feb 14, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until 11:50am to nish this test. You may use one sheet of hand-written
notes an
Statistics 103: Midterm 3
Test Form C
(Dated: March 7, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until noon to nish this test. You may use one sheet of hand-written notes
and
Statistics 103: Midterm 1
Test Form B
(Dated: January 24, 2013)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until 11:50am to nish this test. You may use one sheet of notes and a
calcu
Statistics 103: Midterm 1
Test Form A
(Dated: January 24, 2013)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have until 11:50am to nish this test. You may use one sheet of notes and a
calcu
Statistics 103, Lab 4:
Continuous random variables
Probability density functions
Normal random variables
(
Standardizing: Z = XsdEXX )
()
LAB PROBLEMS
fX ( x) =
1. If Z N (0, 1) what is P (1 Z < 1)?
if a x b;
0 otherwise.
2. (Level 2) Let X N (3, 9). Fin
Statistics 103, Lab 4:
Continuous random variables
Probability density functions
Normal random variables
(
Standardizing: Z = XsdEXX )
()
LAB PROBLEMS
1. If Z N (0, 1) what is P (1 Z < 1)?
Answer: .68
2. (Level 2) Let X N (3, 9). Find:
tomorrow. What is t
Statistics 103, Lab 5:
Dependent random variables
Joint probability mass functions
Conditional PMFs and conditional expected value
Covariance and correlation
var(X + Y ) = var(X ) + var(Y ) + 2 cov(X, Y )
cov(aX, bY ) = ab cov(X, Y )
(b) The marginal dist
Statistics 103, Lab 6:
Using correlation for prediction
LAB PROBLEMS
1. Suppose X and Y are two random variables with
correlation = 0.5 and a football shaped joint
PMF. If you observe that X has a z -score of 1.5
what is your predicted z -score for Y ?
Tr
Statistics 103: Final
Test Form A
(Dated: March 20, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have from 3:30pm to 5:30pm to nish this test. You may use four sheets of
notes and a c
Statistics 103: Final
Test Form B
(Dated: March 20, 2014)
Instructions: Before you do anything, make sure your name, ID and your test form type is on
your scantron. You have from 3:30pm to 5:30pm to nish this test. You may use four sheets of
notes and a c
Statistics 103, Lab 8:
Condence intervals
For each condence interval problem below be sure to rst compute the estimate and the (estimated) standard deviation of the estimate to get a quick and easy idea of where the true population
parameter is. Then foll
Statistics 103, Lab 5:
Dependent random variables
Joint probability mass functions
Conditional PMFs and conditional expected value
Covariance and correlation
var(X + Y ) = var(X ) + var(Y ) + 2 cov(X, Y )
cov(aX, bY ) = ab cov(X, Y )
(b) The marginal dist
Statistics 103, Lab 9:
Hypothesis testing
LAB PROBLEMS
1. (Level 1) A new tranquilizer, given to n = 16 patients, reduced their pulse rate on the average by
4.36 beats per minute with a standard deviation of
0.36 beats per minute. Assuming that such data
Statistics 103, Lab 2:
Probability Mass Functions
Expected value and variance
Practice using probability rules and PMFs
var(X ) = E (X 2 ) (EX )2
Some box model practice
Find P r(W = 0 W = 1), P r(W = 0 W = 1)
and P r(W < 1|W 0) .
LAB PROBLEMS
1. (Level 1