Bilkent University
Fall 2020-21
Math 255 Introduction to Probability and Statistics
Final Exam 7 Jan 2021
• Write your name, student number, and Math 255 section number on
all your answer sheets. Number the sheets.
• The exam consists of four problems. 50 points.
• This is a closed book exam. One A4-size two-sided page of notes is
allowed. No calculators.
• You may receive no credit on correct answers if not fully justified.
Simplify sums and integrals where possible to receive full credit.
• Good Luck.
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:49:41 GMT -05:00
https://www.coursehero.com/file/125679075/Final2020-21Fallpdf/
, 1. [10 pts] Let X1 , X2 , . . . , Xn be independent and identically distributed
(i.i.d.) Bernoulli random variables with
(
p, xi = 1,
pXi (xi ) =
1 − p, xi = 0,
where 0 < p < 1 is a constant. Let Y = X1 + X2 + · · · + Xn .
Compute the conditional probability
P (X1 = x1 , X2 = x2 , . . . , Xn = xn |Y = y)
for every possible value of x1 , x2 , . . . , xn and y. Does your answer
depend on p?
Write your name, student number, and Math 255 section number on all
your answer sheets. Number the sheets. Clearly mark your answer.
You may receive no credit on correct answers if not fully justified.
Simplify sums and integrals where possible to receive full credit.
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:49:41 GMT -05:00
https://www.coursehero.com/file/125679075/Final2020-21Fallpdf/
Fall 2020-21
Math 255 Introduction to Probability and Statistics
Final Exam 7 Jan 2021
• Write your name, student number, and Math 255 section number on
all your answer sheets. Number the sheets.
• The exam consists of four problems. 50 points.
• This is a closed book exam. One A4-size two-sided page of notes is
allowed. No calculators.
• You may receive no credit on correct answers if not fully justified.
Simplify sums and integrals where possible to receive full credit.
• Good Luck.
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:49:41 GMT -05:00
https://www.coursehero.com/file/125679075/Final2020-21Fallpdf/
, 1. [10 pts] Let X1 , X2 , . . . , Xn be independent and identically distributed
(i.i.d.) Bernoulli random variables with
(
p, xi = 1,
pXi (xi ) =
1 − p, xi = 0,
where 0 < p < 1 is a constant. Let Y = X1 + X2 + · · · + Xn .
Compute the conditional probability
P (X1 = x1 , X2 = x2 , . . . , Xn = xn |Y = y)
for every possible value of x1 , x2 , . . . , xn and y. Does your answer
depend on p?
Write your name, student number, and Math 255 section number on all
your answer sheets. Number the sheets. Clearly mark your answer.
You may receive no credit on correct answers if not fully justified.
Simplify sums and integrals where possible to receive full credit.
This study source was downloaded by 100000899606396 from CourseHero.com on 09-25-2025 13:49:41 GMT -05:00
https://www.coursehero.com/file/125679075/Final2020-21Fallpdf/
