Bernoulli Distribution:
P( X = x) = f(x) =p x q1-x
E(X) = p,
x = 0, 1 where q = 1 - p
Var(X) = pq,
Mx(t) = pet + q
Binomial Distribution:
n
P( X = x) = f(x) = p x q n-x
x
x = 0, 1, n
E(X) = np,
Mx(t) = ( pet + q)n
Var(X) = npq,
Geometric Distribution :
P
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Math 230 Final Exam Solutions
Winter Quarter 2012
Monday, March 12, 2012
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Math 230 Test #1
Spring Quarter 2012
Wednesday, April 25, 2012
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Northwestern University
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Math 230 Test #1 Solutions!
Fall Quarter 2012
Wednesday, October 24, 2012
Complete the front page! [1 point!]
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Math 230 Test #2 Solutions!
Fall Quarter 2012
Monday, November 19, 2012
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Write your NetID and your Student ID Number in the spaces provided at
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Math 230 Final Exam Solutions!
Fall Quarter 2012
Wednesday, December 12, 2012
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Math 230 Worksheet #1 Solutions!
October 9, 2012
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Math 230 Test #1 Solutions!
Spring Quarter 2012
Wednesday, April 25, 2012
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Math 230 Worksheet #2 Solutions!
October 16, 2012
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Math 230 Worksheet #3
October 30, 2012
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November 6, 2012
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November 27, 2012
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Question 6. Let C be the curve given by the parametric equations x = et et , y = et .
(a) Show that C is contained on the curve xy = y 2 1, y > 0.
Answer: This follows by just substituting the parametric forms for x and y into this equation. First,
xy = (
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Math 230 Test #1 Solutions!
Fall Quarter 2012
Wednesday, October 24, 2012
Complete the front page! [1 point!]
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Bilkent University
Fall 2016-2017
Math255 Probability and Statistics
Midterm 2
1 Dec. 2016
Problem 1. [5 pts] Let XA , XE , XK be the rainfalls (in cms) in a given year to Ankara,
Eskisehir, and Konya provinces, respectively. Suppose the rainfalls are ind
MATH 255, Summer 2012
D. Aktas
RECITATION FOR MIDTERM 2
Problem 1: Suppose a pair of continuous random variables X andY has a joint PDF that is
Problem 1: (20 points) Consider a pair of continuous random variables (X, Y ) with joint
uniformPDF
overuniform
Math 250 - Quiz 1
Name and section:
Please note that some of these questions are mostly conceptual and for
but may not be necessarily representative of the questions you will encount
Question
Points
1
16
2
4
Total:
20
MATH 255, Fall 2011
D. Aktas
Score
RE
ESE 326-01, Probability and
Statistics for Engineers
Fall, 2005
Instructor: I. Norman Katz
[email protected]
Cupples 2, Room 112
Phone (314) 935-6083
Text: Introduction to Probability and Statistics, Fourth Edition,
by J.S. Milton and J.C. Arnold, McGra
Fall 2015. M250 Homework 1. Solutions.
1. How many ways are there to distribute 10 distinct balls into 4 distinguishable boxes
so that at least one box contains exactly 5 balls?
Solution:
Case 1: Exactly one box contains 5 balls: Choose a box containing 5
2015 Fall. Solutions of M250 Midterm 1 problems.
1a. In how many ways we can order 1 red, 2 white, 3 green and 4 black
balls such that each green ball is on the left of each black ball.
Solution: There is just one possibility to order 3 green and 4 black
Fall 2015. M250. Solutions of Quizzes, 1,2,3. Sections 1,2,3.
1. How many ways are there to distribute 20 identical red and 20 identical white
balls into 12 distinct boxes such that exactly 4 boxes do not contain red balls and exactly
4 boxes do not conta
BILKENT UNIVERSITY
Department of Electrical and Electronics Engineering
EEE212 Microprocessors
QUIZ 3 - SOLUTIONS
21-04-2010
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Section 1
OPEN BOOK, CLOSED NOTES, NO CALCULATORS
Duration: 40 min
12-07-2009 Fall Semester
BILKENT UNIVERSITY
Department of Electrical and Electronics Engineering
EEE212 Microprocessors
QUIZ-3
open book, closed notes, calculators allowed
Duration: 30 minutes
Surname:_
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BILKENT UNIVERSITY
Department of Electrical and Electronics Engineering
EEE212 Microprocessors
QUIZ 3
Section 3
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Open textbook, no calculators.
Duration: 50 minutes
Surname
:
Name
:
ID Number
28-07-2010
BILKENT UNIVERSITY
EEE212 Microprocessors 2010 Summer Semester
Final
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Open TextBook Closed Notes, Calculators Allowed
Use the boxes provided for your answers!
Use comments for reada
13/07/2011
BILKENT UNIVERSITY
EEE212 Microprocessors Sections 1&2
Midterm 2
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Open Textbook Closed Everything Else including
Lecture Notes, No Calculators, No Cellular Phones
USE THE BOXES ONLY
BILKENT UNIVERSITY
Department of Electrical and Electronics Engineering
EEE212 Microprocessors
QUIZ 3
sh is
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12-09-2010 Fall Semester
Open book, closed notes.
Use the boxes provided for your answers
Math255: Probability and Statistics
Bilkent University
Spring 2014-2015
Midterm 1
12 March 2015, 19:30 - 21:10
100 minutes. Three problems. 30 points. Closed book. You may use one one-sided A4size sheet of notes. In each problem, you must show your work i
28-07-2010
BILKENT UNIVERSITY
EEE212 Microprocessors 2010 Summer Semester
Final
sh is
ar stu
ed d
vi y re
aC s
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ou urc
rs e
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Open TextBook Closed Notes, Calculators Allowed
Use the boxes provided for your answers!
Use comments for reada