April 25, 2016
MATH 260 HOMEWORK #7
(Due on Monday, May 2, 2016, submit your assignment to my office by 5:00 pm)
(Please, DO NOT forget to sign and hand in Declaration of Academic Honesty form)
1. A g
Fall 2015. M250 Homework 3: Sample problems for Midterm 1.
(will not be graded, solutions will be sent soon ).
1. How many ways are there to distribute 1 red, 9 identical white and 8 identical
black b
Fall 2016. Solutions of Homework 5 (Midterm 2 sample problems).
1. Let X be a random variable with the density function
1 2 x3
xe 9
3
if x > 0 and
0
otherwise
f (x) =
Find V ar(X 12 ).
Solution: X is
Fall 2016. M250. Solutions of Homework 7.
(Sample Problems for Final Exam).
1. Let X be a normal random variable with EX = 10 and EX 2 = 116.
a) find the density function of Y = (X 10)2
b) find the de
M250. Section 2. Solution of QUIZ 8 (15.12.2016).
1. Let X be a gamma random variable with parameters = 2 and = 1 and given
X the random variable Y is uniformly distributed between X and 4X.
a) Find t
Fall 2016. M250. Homework 7.
(Sample Problems for Final Exam, will not to be graded).
1. Let X be a normal random variable with EX = 10 and EX 2 = 116.
a) find the density function of Y = (X 10)2
b) f
Solution of QUIZ 1. M250 Section 2. (10.10.2016).
1. How many ways are there to distribute 1 red, 1 white and 20 identical blue
balls into 10 distinct boxes such no box is empty?
Solution:
Case 1: red
Fall 2016. M250 Homework 3 ( Sample problems for Midterm 1) Solutions.
1. How many ways are there to distribute 1 red, 9 identical white and 8 identical
black balls into 20 distinct boxes so that exac
Solution of QUIZ 3. M250 Section 2. (24.10.2016).
1. A box contains 8 balls numbered 1, 2, . . . , 8. We randomly remove one ball.
Let X and Y be the smallest and greatest numbers in the box after rem
M250. Section 2. Solution of QUIZ 7 (28.11.2016).
1. Let X be a random variable with the following density function:
f (x) =
1 x2
xe 10
5
if x > 0
0
otherwise
Find VarX 4 .
Solution: X is a Weibull ra
Fall 2016 M250 Homework 2 Solutions.
1. Suppose we have four chests each having two drawers. Chests 1 and 2 have a
gold coin in one drawer and a silver coin in the other drawer. Chest 3 has two gold c
Fall 2016. M250. Solutions of Quizzes, 1,2,3. Sections 1,2,3.
1. How many ways are there to distribute 2 identical red and 20 identical white
balls into 10 distinct boxes such that at least one box is
Fall 2016. M250 Homework 6. Due to Thursday, December 29, 2016.
TIME: 15.30.
1. The random variables X and Y have a joint density function given by:
f (x, y) =
Cxy if 0 x 1, 0 y 1 and
0
otherwise
a) D
Fall 2016. M250 Homework 5: Sample problems for Midterm 2.
(will not be graded, solutions will be sent soon).
1. Let X be a random variable with the density function
f (x) =
1 2 x3
xe 9
3
if x > 0 and
2014 Fall. Solutions of M250 Midterm 2 problems.
1.
Let X and Y be independent random variables having the following
density functions:
C1 sinx if 2 x
0
otherwise
C2 siny if 0 y
0
otherwise
f (x) =
M250 Section 1. Solution of QUIZ 5 (13.11.2014).
1. Let X be gamma a random variable with EX = 24 and V arX = 192. Find EX 3 .
Solution: Let X be gamma random variable with parameters and . Since EX =
October 9, 2015
Bilkent University
Department of Industrial Engineering
IE 262 Self Study Homework Questions- Set 2
Answers will be posted on October 13th, 2015
1. You are given the K and n values of
Fall 2016. M250 Homework 2. Due to Monday, October 31, 2016,
TIME: 16.30.
1. Suppose we have four chests each having two drawers. Chests 1 and 2
have a gold coin in one drawer and a silver coin in the
2016 Fall. Solutions of M250 Final Exam problems.
1. The joint density function of X and Y is given by
3
if 0 x 2, x2 y 4
16
0
f (x, y) =
elsewhere
a) Find the density function of T = max(X, Y ).
Sol
Solution of QUIZ 2. M250 Section 2. (17.10.2016).
1. We toss a fair coin three times. Given that the face H has appeared at
least once find the probability that the face T has appeared exactly once.
S