MATH 355
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Show all your work. The total is 110 points.
1. (10 points) The annual amount Spent for maintenance and repairs in your house has an
approximately n
FOUNDATIONS OF PROBABILITY: EXAM 1. NAME:
Ex 3 (a) State the definition of probability (3 axioms).
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prove to me that yo
(4 points)
Each day, a woman will visit one politically oriented on line chat room among four that she likes.
She is equally likely to visit chat room 1 as chat room 2, and she is twice as likely to v
Warning: You must write/explain each step unless I think (not you think) it is
obvious or you CAN do it mentally. If you don’t do so, you are risking point(s)
deduction unless you can prove to me that
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(15 pts) A survey classified a large number of adults according to whether they were diagnosed
as needing eyeglasses to correct their reading vision and whether they use eyeglasses when
reading
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Chapter 2: Foundations of probability
Oleksandra Beznosova
January 13, 2015
First denitions: Sample space
First denitions: Sample space
A sample space S is a set that includes all possible outcomes
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FOUNDATIONS OF PROBABILITY: HOMEWORK 5.
Ex 4.43 Let X denote a random variable that has binomial distribution with p = 0.3 and n = 5. Find the following values.
(a) P(X = 3)
(b) P(X 3)
(c) P(X 3)
(d)
FOUNDATIONS OF PROBABILITY: HOMEWORK 4.
Ex 4.1 Circuit boards from two assembly lines set up to produce
identical boards are mixed in one storage tray. As inspectors examine
boards, they nd that it is
FOUNDATIONS OF PROBABILITY: HOMEWORK 2.
Ex (a) We have to assign 4 dierent tasks to 4 dierent people in a
group of 10. In how many ways can we do so?
(b) We have to assign 4 same tasks to 4 dierent pe
FOUNDATIONS OF PROBABILITY: HOMEWORK 1.
Ex 2.13 On a large college campus, the students are able to get free
copies of the school newspaper, the local newspaper, and a national
newspaper. Eighty-two p
Chapter 3: Conditional probability and
independence
Oleksandra Beznosova
February 16, 2015
dee
First denitions: Conditional probability
First denitions: Conditional probability
Def If A and B are any
FOUNDATIONS OF PROBABILITY: HOMEWORK 3.
Ex 3.27 A prociency examination for certain skill was given to 100
employees of a rm. Forty of the employees were men. Sixty of the
employees passed the examina
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2.27
2.28
The sample space is (SS, SR, SL, RS, RR. RL, LS, LR, LL}. Let A be the event of at least one vehi-
cle turning left and B be the event that at least one vehicle turns. Assuming equally likel
2.40 Let D =: event that the person has the disease. and T = event ofa test result positive for the disease.
P(D)P{71 D) _ {0.01) (0.90)
P(D)P{710)+P(5)P(n5) ' (0.01) (0.90) + (0.99) (0.10)
P (pl 73
4.57 Let X = amount spent on maintenance and repairs. Then X has a normal distribution with parame-
ters ti = 400, (I = 20 and
_ X_400 450-400
P(X>450) — P[ 20 >_20 ]
z P(Z>2.5) = 0.54.4933 = 0.0062
5.26 Let Y. = number of family homes ﬁres, Y2 = number of apartment ﬁres, and Y3 = number of ﬁres in
other types of dwellings, out of 4 ﬁres. Then (Yl, Y2, Y3} has a muitinomial distribution with
para
1 1 1/2 I l/Z 33‘] 15 21
5.9 a. P[X1<§,X2> Z ] = In [1/4(x|+x2]dx2dxl : J‘o [T4, 5 dxl = a
2
_x x
b- = I (11+x2)dx2dxl = [x1x24—Ez]
f,(x1}f2(x2) = [xl+ l ][x2+ ¢x1+x2=f(xl,x2)
forOSx, $1,03xgsi.
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