Chapter 2.1: Systems of Linear Equations
A linear equation is an equation in which each variable has degree one. We call them linear because when a linear equation involves only two variables, the equation describes a straight line. Examples: Here are so
Mathematics 452 [F01]: Stochastic Processes Department of Mathematics and Statistics, University of Victoria Fall, 2010 INSTRUCTOR: Boualem Khouider (khouider@uvic.ca) Social Sciences & Math Building A550, Phone: 250-721-7439 (to use only in case of emerg
Math 452/550: Stochastic processes Homework assignment # 1 Due September 24th, 2010
Submit all of your work for marking. You are permitted to collaborate on the homework; however, you must write up your homework yourself. You should not copy somebody else
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UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 PRACTICE TEST 2 Instructor: Dan Pollock Maximum score: 20 marks Duration: 50 minutes
Name:
Student No.:
Instructions: (a) Use HB (or softer) pencil to blacken completely the appropriate circle
UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 SIT-DOWN PRACTICE TEST 2, NOVEMBER 19 Instructor: Dan Pollock Maximum score: 20 marks Duration: 50 minutes
Name:
Student No.:
Instructions: (a) Use HB (or softer) pencil to blacken completely
UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 SIT-DOWN PRACTICE TEST 2, NOVEMBER 19
Question 1. You roll a fair 4 sided die twice and multiply the numbers showing on the top face of each roll. What is the expected value of this experiment
UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 PRACTICE TEST 2 SOLUTIONS
Question 1. A casino operates a game where the player ips a coin and rolls a 6 sided die. If they get a heads and roll a 4, 5 or 6, they win $20. If they get a tails
UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 PRACTICE MIDTERM 1 SOLUTIONS, OCTOBER 8
Question 1. You draw 3 cards from a fair deck of 52 cards. Given that the rst card is a heart and the second card is a spade, what is the probability th
8.4: The Binomial Distribution
Another important type of random variable for which we have a formula for P (X = x) is called the binomial random variable. If X is a binomial random variable, then it has the following characteristics: The experiment consi
Chapter 7.3: Rules of Probability
In the last class, we learned two important facts about probability. If E is an event in a uniform sample space S then: 0 P (E ) 1 AND n(E ) n(S )
P (E ) =
Today, we will use these facts to nd out some more rules about
Chapter 7.4: Counting Techniques and Probability
In many probability problems, the sample space S is too large to count simply by listing all sample points. If this is the case, we may use our dierent counting techniques (i.e. permutations, combinations,
Chapter 7.5: Conditional Probability
In some cases, we may perform an experiment, and already know something about the outcome. For example, suppose I had a bag containing 5 red marbles and 5 green marbles. My experiment will consist of selecting two mar
Chapter 7.5 Part Two: Independent Events
In many cases, knowing the outcome of one event does not provide any information for a second event, or aect the probability of the second event occurring. For example, suppose we were to roll two dice, and were c
Chapter 7.6: Bayes Theorem
We have seen how occurrences of event in the past can aect probabilities of future events, and we learned how to calculate these probabilities using the conditional probability formula. There are occasions where we may wish to
Chapter 8.1: Random Variables
A random variable assigns a number to each outcome of an experiment. We use a random variable when we have an experiment where the outcomes may be counted or measured. Suppose two dice are rolled. Let the random variable X d
Chapter 8.2: Expected Value
Suppose we were to repeat an experiment many times. We might be interested in the average value of our random variable. For example, consider a game where we might either earn or lose money each time we play. Suppose our rando
Handbook 5: The Hypergeometric Distribution
There are several types of random variables for which we can create a formula to nd P (X = x), rather than needing to construct the complete probability distribution table. One such type is called the hypergeom
UNIVERSITY OF VICTORIA MATHEMATICS 151, SECTION A02, FALL 2008 MIDTERM 1 SOLUTIONS, OCTOBER 10
Question 1. A student must answer exactly 15 out of 20 questions on an exam. If the student must answer at least 8 of the rst 10 questions, how many choices doe
Functions of Several Variables
A function of two variables is a rule that
assigns to each ordered pair of real numbers (x, y)
in a subset D of the plane a unique real number
denoted by f (x, y). The set D is the domain of f
and its range is the set of val
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MATH 377 Practice Midterm
R. Edwards
Your name:
Your student no.:
You may use books, notes, calculators.
Please be sure to show sucient work to justify your answers.
Total marks on the test: 25
Marks
1. In our Voronoi-based model of crystal growth assume