~/ Math 3 51 - Homework 8
Due i n c lass o n T hursday.
October 5, 2010
1. (This comes partially from problem 18 i n the text.) A t otal of 46% of the people eligible to vote in a certain city classify themselves as Independents, 30% as Liberals an
Chapter 7 summary Properties of Expectation
Expectation of a function of a pair of random variables: Recall from Chapters 4 and 5 that if X is a random variable, then its expectation is given by E [X ] = and if g (x) is any real-valued function E [g (X )
Chapter 6 summary Jointly Distributed Random Variables
Basic problem: Let X and Y be random variables. Consider the pair (X, Y ). This is not a random variable because it isnt a real-valued function (since its values are in R2 , not R). However, if D is
Chapter 5 summary Continuous Random Variables
Denition of a continuous random variable: A random variable called continuous (it is also called absolutely continuous) if there exists a function fX with the property that for any two numbers a, b with a < b
Chapter 4 summary Random Variables
Denition of random variable: A random variable is a function that assigns a real number to the result of a random experiment. Thus it is a function whose domain is the sample space of the experiment and whose range is c
Chapter 3 summary Conditional Probability and Independence
Denition and basic formula for conditional probability: Let A, B be two events. If the probability that B occurs is positive, then P (A|B ) = P (A B ) . P (B )
In words, it is the probability tha
Chapter 2 summary Axioms of Probability
Discrete sample space: Suppose we have an experiment for which there are either a nite or countably innite set of possible elementary outcomes. The set S consisting of all of the possible elementary outcomes is cal
Chapter 1 summary Combinatorial Analysis
Fundamental counting principles: 1. (multiplication principle) Say task 1 can be done in n1 ways, task 2 can be done in n2 ways, ., task k can be done in nk ways. Then if we wish to do all the tasks in sequence, i
Math351 Spring 2010
Final review
Warning: this is rather a review of the course than a review before the nal exam. Consider it as a supplement to the excellent end-of-chapter reviews in the Rosss book. This review consists of two parts: (1) A short list o
Math 351 W.T. Kiley
Clearly show your work and answers. Follow the Honor Code.
Exam2
December 2h 2009
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of 10 and a variance of 25. Find: a) the probability that X is between 7 and 13;
X is normal with
a mean
t
b) an interval that has .92 probability o
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M ath 3 51 - Homework 1 3
Due i n c lass o n T hursday.
Nov. 2 ,2010
1. Let X b e t he c ontinuous r andom v ariable t hat r epresents t he a mount o f g asoline (in t housands o f g allons) t hat a filling s tation sells p er week. Say i ts p r
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M ath 3 51 - Homework 1 2 D ue i n c lass o n T uesday.
October 28, 2010
B efore d oing t hese p roblems, r ead t he C hapter 4 s ummary, i n p articular t he e ntries c oncerning g eometric r andom v ariables a nd n egative b inomial r andom v ariab
Math 3 51 - Homework D ue i n c lass o n T uesday.
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1. An c ontains t hree b lue, four red, o ne g reen, two black, a nd five yellow balls. T ake a b all, n ote i ts color, p ut i t b ack in t he the u rn, a nd t hen r epeat five more t imes (so
September 28, 2010
Math 351 - Test 1
1. Suppose we have ve identical red books, six identical green books, and three dierent yellow books. (a) In how many dierent ways can they be arranged on a shelf? (b) In how many dierent ways can they be arranged on a
October 1, 2010
M ath 3 51 - Homework 7
1. Suppose we have t hree c ards. T he first is red on b oth sides, t he second is b lue o n b oth sides. a nd t he t hird is r ed Oil olle side a nd blue 011 t he o ther. Label t he sides of t he first c ard a s
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M ath 3 51 - Homework 6 D ue i n c lass o n T hursday.
September 21, 2010
1. If y ou select eight cards from a s tandard deck of 52 cards, w hat is t he p robability you g et two of one denomination, two of a nother d enomination, t hree o f a t hi
S eptember 16, 2010
M ath 3 51 - Homework 5
Due i n c lass o n T uesday.
L Say we have 20 c ards: 5 are blue (color 1) a nd n umbered 1 t o 5, 5 a re green (color 2) a nd l lumbered 1 t o 5, 5 a re red (color 3) a nd n umbered 1 t o 5, 5 are yellow (
September 14, 2010 M ath 3 51 - Homework 4
Due i n c lass o n T hursday.
1. Three sets A, B , C which lie in a sample space S satisfy t he following:
P (A) .3 P (B) = .33 P (C) .17 P (AB) .08 P (AC) = .07 P (BC) = .1 P (A C BCC C ) .4
~t : PCA~C.c/:.
S eptember 9, 2010 M ath 3 51 - Homework 3
Due i n c lass o n T hursday.
In e ach o f t hese p roblems s how e xactly w hat i t i s y ou a re c alculating a nd t hen c omplete t he c alculation u sing a c alculator. I t's o k t o a nswer e ach q uesti
S eptember 7, 2010
M ath 3 51 - Homework 2 D ue i n c lass o n T hursday. I n e ach o f t hese p robJems s how e xactly w hat i t i s y ou a re c alcuJating a nd t hen c omplete t he c alculation u sing a c alculator. I t's o k t o a nswer e ach q uestion
S eptember 3, 2010
M ath 3 51 - Homework 1
Due i n c lass n ext T uesday.
In e ach o f t hese p roblems s how e xactly w hat i t i s y ou a re c alculating a nd t hen c omplete t he c alculation u sing a c alculator, f or e xample (
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4 0. I t's
December 2, 2010
Math 351 - Test 3
1. An urn has two black and one white ball. An experiment consists of taking two balls from the urn. Call it success if both of them are black and call it failure if they are not both black. After you have chosen the two
October 31, 2010 Math 351 - Test 3 Some comments on the test.
1. Problem 1: (a) Most correctly deduced that p = 1/3. You should view it as an urn problem. You can then calculate p either by using combinations, or by conditional probability (it is the prob
October 28, 2010
Math 351 - Test 2
1. Suppose urn I has one red and three blue balls; suppose urn II has one red and ve blue balls. Pick one ball from each urn. You get $2 for each red one and $1 for each blue one. Let X be the total number of dollars you
M ath 3 51 - Homework 9
Due i n c lass o n T hursday.
1. An u rn c ontains balls n umbered 1 t o 10. B alls n umhered 1,2,4.6.7.9 a re hlue; balh:; n umhered 3,5.8 a rc red: ball n umber 10 is green. A single ball is chosen. Let B " it is hlnc", R =