SOLUTION
STT441 QUIZ 4
NAME
ID
The following relates to problems 1-4: The density of a continuous random variable X
is
Problem 1.
1. .15
Find P(.4 X .6)
2. .21
3. .37
4. .41
5. .1
3. .37
4. .41
5. .75
3. .37
4. .41
5. .75
Problem 2. Find E (X )
1. .15
2.

STT441
SOLUTION
NAME
ID
1. What is the probability of getting exactly 2 heads if you flip a fair coin 5 times?
(a) .31 (b) .41 (c) .51 (d) .61
5 5
(.5) .31
2
2. A box contains 50 parts, 3 which are defective. An inspector chooses, without
replacement,

Quiz 2.
SOLUTION
Name:
ID number
Problem 1. A urn contains 5 white and 7 black balls. Two balls are randomly selected.
(1) Assume that the sample is without replacement. Find the probability that they
are of the same color.
a .51 b .49 c .47 d .53 e. none

Solution
Stat 441
Quiz 3
1. A coin lands on heads 30% of the time. We flip the coin twice.
Let A ( H , H ) and B (T , H ) .
a. P(A)
(1) .15 (2) .09 (3) .42 (4) .49
b. P( B | Ac )
(1) .15 (2) .09 (3) .42 (4) .23
Explanations
a. P( A) P( H ) * P( H ) .3 *

Solution to Homework 6
1. [6-2] Suppose that 3 balls are chosen without replacement from an urn consisting of 5 white
and 8 red balls. Let Xi equal 1 if the ith ball selected is white, and let it equal 0 otherwise. Give
the joint probability mass function

STT441 QUIZ 5
SOLUTION
NAME
ID
Let (X,Y) be uniformly distributed on the triangle generated by the points (0,0), (1,0) and
(1,1). More formally the joint pdf is given by f ( x , y ) C , 0 y x 1 , where C is a
number. Hint: Observe:
If x is fixed then 0 y

STT 441
QUIZ 1
NAME:
1. We wish to distribute 10 distinguishable gifts to 3 winners A, B and C.
(a) How many division are possible such that A receives 3 gifts, B receives 4
gifts and C receive 3 gifts?
[3pts]
10!
= 4200.
3!3!4!
(b) If we choose 7 gifts o

Homework 3 Solution
1. [3-5] An urn contains 6 white and 9 black balls. If 4 balls are to be
randomly selected without replacement, what is the probability that the
rst 2 selected are white and the last 2 black?
Let A =cfw_the rst 2 selected are white and

Solution to Homework 4
1. [4-4] Five men and ve women are ranked according to their scores on
an examination. Assume that no two scores are alike and all 10! possible
rankings are equally likely. Let X denote the highest ranking achieved by
a woman. (For

Solution to Homework 5
1. [5-2] A system consisting of one original unit plus a spare can function
for a random amount of time X. If the density of X is given (in units of
months) by
Cxex/2 x > 0
f (x) =
0
x0
what is the probability that the system functi

Homework 2 Solution
1. [2-3] Two dices are thrown. Let E be the event that the sum of dice is
odd. let F be the event that at least one of the dice lands on 1, and let
G be the event that the sum is 5. Describle the events EF , E F , F G,
EF c and EF G
So

STT441
Probability
September 21, 2015
Homework 3 for STT 441: p 102 - 107, questions 5, 8, 11, 12, 26, 50, 59
Due in on the 9th of October, Friday, just before the lecture begins.
Please read sections 3.1 to 3.4 in the textbook
Further practice for yourse

STT441
Probability
September 9, 2015
Homework 1 for STT 441: Q 7, 8, 15, 23, 27 on p 16 - 17
Further practice for yourself - no need to submit - Q 1, 2, 3, 4, 5, 10, 19 on
p 20 - 21.
Due in on 09/11/15 just before the lecture begins.
1

Midterm Exam
1. A committee of 7 is to he randomiy seiected from a group of 6 men and 4 women.
What is the probability that the committee consists of
(a) 4 men and 3 WOI‘ﬂGi‘i;
(b) 3 men and 4 women?
Solution. The probabilities desired are giveh by
(Stilt

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of the fégﬁlators,
and one
Timothy Geithner, detest each other and refuse to serve togeizher?
/ '33.]?! af-M: hm ~:Di.w\M CEO; (¥{+rc we.

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STT441
Probability
September 14, 2015
Homework 2 for STT 441: p 50-54 Q 3, 6, 9, 12, 15, 45, 52
Due in on 25th of September, Friday, just before the lecture begins.
Please read sections 2.1 to 2.5 in the textbook
Further practice for yourself - no need to

September 12, 2015
STT441 Homework 1 solutions
7 a. This is a permutation problem. The total is 6!.
b. Consider 3 girls and 3 boys as 2 objects. There are 2! ways to arrange
these 2 objects. Then we permute all the girls and all the boys in each group,
se

STT 441- SECTION 1
PROBABILITY AND STATISTICS-1
Fall 2014
Instructor: Aylin ALIN
e-mail: [email protected]
Office: C 419 Wells Hall
Office Hours : MW F 10:00 AM-11:00 AM and by appointment
Lecture Times: M W F 3:00 PM 3:50 PM
Lecture Room: A218 Wells Hall

Homework 3 Solution
1. [3-5] An urn contains 6 white and 9 black balls. If 4 balls are to be
randomly selected without replacement, what is the probability that the
rst 2 selected are white and the last 2 black?
Let A =cfw_the rst 2 selected are white and

Homework 2 Solution
1. [2-3] Two dices are thrown. Let E be the event that the sum of dice is
odd. let F be the event that at least one of the dice lands on 1, and let
G be the event that the sum is 5. Describle the events EF , E F , F G,
EF c and EF G
So