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Assignment 3 (due Sunday, 25 November 2018 at 23:55)
students decide to form a group, they have to solve the union of the students’ assigned problems.^ •^ This assignment is to be completed by teams of one, two or three students. If two or three
• Your assigned problems are determined by the last digit of your student ID number:
Last digit of ID number Assigned problems 0 0, 1 1 1, 2 2 2, 3 3 3, 4 4 1, 3 5 0, 2 6 1, 4 7 0, 3 8 2, 4 9 0, 4
• If the assignment is handed in during the 24 hours following the deadline, it will lose 25
points. If it is handed in during the next 24 hours, it will lose another 25 points and so on.Consequently, no points can be gained after 4 days.
hand-written material. You must only submit the Word document, and in Word or pdf format, to^ •^ The answers must be typed, not handwritten. Do not attach Excel or other printouts or
Moodle.
• Moodle has a 1MB size limit for students uploads (such as assignments). In order to
reduce file size, you can use the "Reduce File Size" in the File menu Word.
• E-mailed assignments will not be accepted. You must upload your assignment to Moodle.
It is sufficient for one person to upload the answers for each team.
points.^ •^ SHOW YOUR WORK. You may skip the details. Answers without derivation will not get
Team member names and ID’s: Last Name First Name ID
1. SUİLETEN GÜLŞAH 2016300183 2. KAÇMAZ SELİM YAVUZ 2016300093 3. ÇARKÇI BARIŞ 2016300261
QUESTIONS
0. There is a shoe in a pond. It is either a right shoe or a left shoe, with equal probability. I then throw
in a left shoe into the pond. Afterwards I fish out a shoe, and it turns out to be a left shoe. What is the probability that the shoe which is still in the pond is a left shoe, too?
1. A student turned in an assignment by leaving it in my department mailbox without a name. Since
all the other students already turned in their assignments, I know that this student is either Armağan or Bülent, with equal probability. Upon further inspection, I notice that the assignment was done with a green pen. Only 10% of students use green pens. I know that Armağan writes with a green pen, but I don’t know if Bülent writes with a green pen or not. Given that the assignment was done with a green pen, what is the probability that Armağan was the student who left the assignment in my mailbox?
A. Event that the assignment is Armağan’s.
B. Event that the assignment is Bülent’s.
G: Event that the assignment is written by a green pen. P(A) = P(B) = 0. P(A | G) =? P(A|G) = P(G|A) * P(A) / P(G) P(G|A) = 1 and P(G) = P(G|A)*P(A) + P(G|B) * P(B) = 1 * (0.5) + (0.1) * (0.5) = 11/ Hence, P(A|G) = P(G|A) * P(A) / P(G) = 1 * (0.5) / (11/20) = 10/
2. The Statistics exam is going to be difficult, normal, or easy. The probability that I solve a question
on a difficult exam is 30%, on a normal exam it is 50%, and on an easy exam is 90%. These probabilities are valid for each of the questions on the exams, independent from one another. You take the exam and solve the first question. What is the probability that you will also solve the second question?
G. G. AkinEC 233Fall 2018
Exponential distribution with E(Y) = β = 10.
P(Y > 15.000) = dy
= 1/ 10.000 dy.
Let’s say -y/10.000 = u. Hence,
du/dy = -1/10.000 and dy= -10.000du.
= 1/10.000 (-10.000) du
= du
= - = = 1 / (e )
Now, question becomes geometric probability distribution with p = 1 / (e )
Hence, E(Y) = 1/p = 1/ [1 / (e ) ] = e.
G. G. AkinEC 233Fall 2018
