Fin 9762
Final Exam
Prof. Piskula
2026-05-18
Write your commitment to academic honesty. In your own words, include a commitment to
submit only your own work and to not supply others with help. (1 point deducted if missing.)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
Signed ______________________________________ Date __________
Print Name___________________________________
Do NOT begin until instructed to do so.
Version Γ
No one will be permitted to leave the room and return to continue working on
their test.
There will either be assigned seats or some students may be randomly moved
to different seats before the test.
No electronic devices are permitted for this test. All watches must be
removed. Any presences of electronics, including looking at your telephone in
the classroom after the test is over, and of course taking pictures, will be
considered a violation of academic integrity.
Be sure to indicate your answers clearly, or you will not receive credit.
Penmanship, grammar and neatness will affect the grade.
There is a penalty of two points for any students that separates the pages of
the test, including separating the tables from the rest of the test.
,Fin 9762 Name:____________________________________
Final Exam, Prof. Piskula
All questions are one point unless otherwise noted. There are 25 points in total.
S&W Chapter 2 – Review of Probability
SW 2-1. (2 points) (instructor created) Calculate the marginal distributions of X and Y below.
Calculate E(X) and E(Y). Calculate the 8 conditional probabilities and enter them in the spaces
provided. Demonstrate that X and Y below are independent or are not independent (so have a
conditional relationship).
E(X) = 2/3 E(Y) = 3/4
Y
0 1
0 1/12 3/12
X
1 2/12 6/12
P(X=1|Y=0) = __2/3__ P(X=1|Y=1) = _2/3__
P(X=0|Y=0) = _1/3___ P(X=0|Y=1) = _1/3__
P(Y=0|X=1) = _1/4___ P(Y=1|X=1) = 3/4___
P(Y=0|X=0) = _1/4___ P(Y=1|X=0) = 3/4___
Are the variables independent or conditional? Why?
Independent since all joints are products of their marginals, and all conditionals equal the
marginals.
, SW 2-2. (1.5 points) (instructor created) Recreate the grid of formulas for mean/expected value,
variance, covariance, and correlation. Arrange the formulas in four columns: theory (expected
value format), when you have the probabilities, when you have all the observations, and when
you have a sample. Consider using a landscape orientation.
See table.
Final Exam
Prof. Piskula
2026-05-18
Write your commitment to academic honesty. In your own words, include a commitment to
submit only your own work and to not supply others with help. (1 point deducted if missing.)
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
___________________________________________________________________________
Signed ______________________________________ Date __________
Print Name___________________________________
Do NOT begin until instructed to do so.
Version Γ
No one will be permitted to leave the room and return to continue working on
their test.
There will either be assigned seats or some students may be randomly moved
to different seats before the test.
No electronic devices are permitted for this test. All watches must be
removed. Any presences of electronics, including looking at your telephone in
the classroom after the test is over, and of course taking pictures, will be
considered a violation of academic integrity.
Be sure to indicate your answers clearly, or you will not receive credit.
Penmanship, grammar and neatness will affect the grade.
There is a penalty of two points for any students that separates the pages of
the test, including separating the tables from the rest of the test.
,Fin 9762 Name:____________________________________
Final Exam, Prof. Piskula
All questions are one point unless otherwise noted. There are 25 points in total.
S&W Chapter 2 – Review of Probability
SW 2-1. (2 points) (instructor created) Calculate the marginal distributions of X and Y below.
Calculate E(X) and E(Y). Calculate the 8 conditional probabilities and enter them in the spaces
provided. Demonstrate that X and Y below are independent or are not independent (so have a
conditional relationship).
E(X) = 2/3 E(Y) = 3/4
Y
0 1
0 1/12 3/12
X
1 2/12 6/12
P(X=1|Y=0) = __2/3__ P(X=1|Y=1) = _2/3__
P(X=0|Y=0) = _1/3___ P(X=0|Y=1) = _1/3__
P(Y=0|X=1) = _1/4___ P(Y=1|X=1) = 3/4___
P(Y=0|X=0) = _1/4___ P(Y=1|X=0) = 3/4___
Are the variables independent or conditional? Why?
Independent since all joints are products of their marginals, and all conditionals equal the
marginals.
, SW 2-2. (1.5 points) (instructor created) Recreate the grid of formulas for mean/expected value,
variance, covariance, and correlation. Arrange the formulas in four columns: theory (expected
value format), when you have the probabilities, when you have all the observations, and when
you have a sample. Consider using a landscape orientation.
See table.
