This document outlines the instructions for the EC 233 Final Exam for Fall 2020. It states that students must answer one of two questions and provides details for submitting answers. The questions involve portfolio management, probability density functions, and joint distributions. Students are instructed to show their work and reasoning in a clear manner. The deadline to submit is February 12 at 11:59 PM.

1. EC 233 Final Exam, Fall 2020
Ozan Hatipoğlu
Answer question 1 and choose one of second or third question.
( 2 total). Each
question has the same points (50) but a different degree of
difficulty and a time penalty. The
earlier you post the higher the grade you will get out of its
potential. If you submit as late as still
possible( example: submitting 1 second earlier than the
deadline) at most x points will be
subtracted out of total. The penalty , x, is linear in time
passed. You can not submit twice.
Make sure everything is OK before you click the submit button.
No questions about any of
the details of this exam will be answered. If you think a
question is wrong, misleading or
missing necessary info, just state it in your answer. Upload 1
pdf file with handwritten answers.
You can use R , Excel or other software. By submitting you
agree that you accept the honor code
in Midterm. Deadline: February 12, 23.59:00 PM.
1) (x= 5) You are a portfolio manager. You observe that two
normally distributed asset returns,
" and " have the same mean, " , and the same variance, ! , but
are independent. Given
that " find the mean and riskiness (variance) of the return of
the
portfolio, R, that consists " of Asset 1 where " and " of
Asset 2 where " , i.e.

2. (R =a" +b" ) and " . First determine " randomly by selecting
from a uniform
distribution between (0,1), (" ), then solve the question. Write
all the details of the steps
that you actually went through while solving this exercise in a
very clear manner.
2) (x= 15) , Choose two numbers, " and " randomly between
0 and 1000 and determine c
such that " serves as a continuous probability density function
for " where " .
Using " , calculate " and " .
3) (x=5) Given the joint distribution
" , find a possible value for " first.
Then determine one number b randomly in any meaningful way
you like. (" and calculate
i)"
ii )" - "
Make sure to write down all the details that you actually went
through while solving this
exercise in a very clear manner.
R1 R2 μ σ
P (R1 < 0.05) = 0.2,
a 0 < a < 1 b 0 < b < 1
R1 R2 a + b = 1 a
b = 1 − a
n1 n2

3. f (x) = c x x n1 < x < n2
f (x) = c x E (2x + 1) v a r (2x + 1)
f (x1, x2) = a x1x2 f or 0 < x1 < 1, 0 < x2 < 1, a n d 0 el s e wh
er e a
b ≠ 0)
P (b X1 + b X2 ≤ 1)
E (X1 ∣ X2 = 1) (E (X1 ∣ X2 = 0.5))