Math 302. Assignment 7
Due Mar. 9
Exercises from the textbook (Grinstead & Snell 2nd revised edition)
1. Section 5.2 (p.219) Ex. 2
2. Section 5.2 Ex. 14
Note: the point P is chosen uniformly at random in the unit square [0, 1]2 , so to
find the probabilit
Sample midterm
1. (a) Find the probability that a five card poker hand contains exactly
3 aces.
(b) Find the probability that a five card poker hand contains at least
3 aces.
(c) Let A and B be events such that P(A) = 0.6, P(B) = 0.3 and
P(A B) = 0.8. Fin
1
c Anthony Peirce.
Introductory lecture notes on Partial Differential Equations -
Not to be copied, used, or revised without explicit written permission from the copyright owner.
Lecture 29: The heat equation with Robin BC
(Compiled 3 March 2014)
In thi
c Anthony Peirce.
Introductory lecture notes on Partial Differential Equations -
Not to be copied, used, or revised without explicit written permission from the copyright owner.
1
Lecture 30: Sturm-Liouville Problems involving the
Cauchy-Euler Equation -
c Anthony Peirce.
Introductory lecture notes on Partial Differential Equations -
Not to be copied, used, or revised without explicit written permission from the copyright owner.
1
Lecture 26: Circular domains
(Compiled 3 March 2014)
In this lecture we co
1
c Anthony Peirce.
Introductory lecture notes on Partial Differential Equations -
Not to be copied, used, or revised without explicit written permission from the copyright owner.
Lecture 13: Full Range Fourier Series
(Compiled 3 March 2014)
In this lect
Math 302, assignment 6
Due Oct. 26
1. Suppose
R X is a continuous random variable and X 0 always. Let F be its CDF. Show that
EX = 0 1 F (t)dt. (Hint: use integration by parts.)
Bonus: Show this also for discrete positive random variables.
2. a. For the f
Math 302, assignment 5
Due Oct. 19
Note: the last WebWork assignment was extended to this week.
1. A random variable has density f (x) = cx3 on [2, 5]. Find c, find the CDF F (t) and find P(X 4).
2. A dice is thrown. If the result is Y , then we let X be
Math 302 Sample exam
Instructions
Explain your reasoning thoroughly, and justify all answers (even if
the question does not specifically say so).
No aids are permitted (calculators,notes,etc).
A formula sheet is provided (see piazza and online).
Questi
Math 302, assignment 10
The conditional expectation E(X|Y ) is defined as
continuous case.
Due Nov. 30
P
xp(x|y) in the discret case and
R
xf (x|y)dx in the
1. X, Y have joint density 21 yeyx/y for x, y > 0 and 0 if either is negative.
a. Find the margina
Math 302, assignment 10
Due Nov. 23
Note: there are questions on WebWork as well.
The correlation of variables X, Y is defined by
(X, Y ) =
Cov(X, Y )
.
Var X Var Y
It measures how linearly dependent variables are.
1. Show that if Y = aX + b for some fix
Math 302, assignment 11
Do not hand in.
1. If X is the sum of 100 six sided dice, what does Chebyshevs inequality say about P(X < 300)? What
is the CLT approximation?
2. Suppose each customer at a store pays on average $12, and the variance is 52 . If the
Math 302, assignment 7
Due Nov. 2
Note: A few questions on WebWork.
1. If X is a N (0, 1) r.v., find the p.d.f. of X 2 . (Hint: use the CDF).
p
1/
|X|. (Hint: same as for 1.)
2. If X is a Cauchy r.v. (density 1+x
2 ), find the p.d.f. of
3. a. Prove that i
Math 302, assignment 8
Due Nov. 18
Note: A few questions on WebWork.
1. A dartboard centered at the origin has radius 6. Let (X, Y ) be the random location of a dart thrown
by a competent player. Assume X and Y have joint probability density function
(
p
Math 302, assignment 4
Due Oct. 12
Note: there are several questions on WebWork for this week as well.
1. An experiment is repeated, and the first success occurs on the 8th attempt. What is the success
probaility for which this is most likely to happen? (
Math 302, assignment 5
Due Oct. 19
Note: the last WebWork assignment was extended to this week.
1. A random variable has density f (x) = cx3 on [2, 5]. Find c, find the CDF F (t) and find P(X 4).
R5
solution. We have 2 cx3 dx = 1, which gives c(54
Rt
CDF
Math 302, assignment 0
Due Sep. 16
This assignment is not for credit. It is concerned with some material from prerequisite courses (calculus,
220). If you wish to have your work checked, hand it in by Friday.
Suggested reading related to this: Appendice
Math 302, assignment 3
Due Oct. 5
1. a. Suppose events A, B, C are independent, and have probabilities 1/2, 1/3, 1/4 respectively. What is
P(A B C)?
b. Suppose now that we only know that each pair of A, B, C is independent. Prove that
19
17
P(A B C)
.
2
Math 302. Assignment 9
Due Mar. 23
Exercises from the textbook (Grinstead & Snell 2nd revised edition)
1. Section 5.2 (p.222) Ex. 26
2. Section 5.2 Ex. 37
Note: In the next exercises (3,5,6,7, not 4) you have to use the half-integer correction. If the tab
Math 302. Assignment 10
Due Mar. 30
Exercises from Ross textbook this time (slightly modified)
1. A bin of 4 transistors has 2 defective ones. You repeatedly take (without replacement) transistors out of the bin and test them. Let N1 be the rank (in [1.4]
Math 302. Assignment 8
Due Mar. 16
Exercises from the textbook (Grinstead & Snell 2nd revised edition)
1. Section 2.2 (p.72) Ex. 6
2. If X is an exponential random variable with parameter , and c > 0, show that
cX is exponential with parameter /c.
3. If X
Math 302. Assignment 4
Due Feb. 10
Exercises from the textbook (Grinstead & Snell 2nd revised edition)
1. Section 4.1 (p.154) Ex. 32
Note: we assume that the passable/non-passable status of different roads are independent.
2. Section 4.1 Ex. 43
hint: the
Math 302. Assignment 1
Due Jan. 20
Exercises from the textbook (Grinstead & Snell 2nd revised edition)
1. Section 1.2 (p.35) Ex. 6
Hint: there is a certain C > 0 (to be determined) such that the distribution function
is of the form m(i) = C i for i = cfw_
Math 302. Assignment 3
Due Feb. 3
Exercises from the textbook (Grinstead & Snell 2nd revised edition)
1. Section 3.2 (p.115) Ex. 20
2. Multinomial coefficients
For m 1 and n1 , . . . , nm positive integers, with the notation n for the sum
n1 + + nm , deno
Top Ten Summation Formulas
Name
1.
Binomial theorem
Binomial series
Summation formula
!
n
X
n
xnk y k
(x + y)n =
k
k=0
!
k
2.
Geometric sum
X
integer n 0.
ar k = a
ar k =
k=0
3.
Telescoping sum
|x| < 1 if 6=
n
k=0
Geometric series
integer n 0
k
x = (1 +
Problems from Chapter 3 Handout:
13. A die is rolled three times. What is the probability that you get a larger number
each time?
Since only one permutation will be strictly increasing of the 6 possible from
MATH 302 INTRODUCTION TO PROBABILITY SUPPLEMENT
Elementary calculus and some special functions
In this supplement we discuss some important mathematical concepts that you need to
know.
Differentiation and integration.
Principle 1 [Differentiating a polyno
lOMoARcPSD
Seminar assignments, Questions and answers
Applied Linear Algebra (The University Of British Columbia)
Distributing prohibited | Downloaded by Yilei Jiang (jiangyilei9538@gmail.com)
lOMoARcPSD
Math 307: Problems for section 1.1
1. Use Gaussian
Tues. Feb. 9
Traits (Ch. 5)
Objectives
- Personality stability
- Rank order
- Mean level
- Personality change
- Personality coherence
Think About "You"
- Think about your personality when you were 5 y
Tues. Mar 1-Thurs. Mar 3
Cognition(Ch. 12)
Objectives
Behaviorism
-Influence of personality
Cognition
-Influence on personality
Perception differences
-field dependence and independence
-pain tolerance
What is cognition?
-Simple definition: thinking
-more
PSYC 301 Midterm 2 Reading Objectives
Epilepsy
Hustvedt (2013)
Review: Philosophy Matters in Brain Matters
1. Discuss the degree to which Cartesian dualism still haunts modern medicine and neuroscience
- Although most neuroscientists and physicians would