Stat 211 - Tutorial 1
1. A closing price (in dollars) at Dec 31, 2011 of 30 stocks in a portfolio are given below: 52.78 55.88 51.12 48.27 40.72 52.39 49.82 51.69 54.59 55.85 47.59 52.48 54.60 57.19 49.04 52.87 54.83 53.34 52.85 50.21 50.49 54.48 49.54 49
Eduardo Martin-Martinez - Math 211 Sec 1
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The Laplace Transform
The Laplace transform is a linear mathematical transformation (takes functions as an input and returns
functions as an output)
The Laplace transform is denoted as L cfw_f (t). It takes as an
Eduardo Martin-Martinez - Math 211 Sec 1
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The Harmonic Oscillator
There is a physical reason why second order linear ODEs with constant coefficients are worth studying. These
equations model one of the most important systems in physics (and in engineerin
Eduardo Martin-Martinez - Math 211 Sec 1
Solving the example that we saw in class
Consider the following equation
y =
3t2 + 6ty 2
6t2 y + 4y 3
We can rewrite it in terms of a 1-form (or, with a little less of rigour, using that y = dy/dt and
multiplying
When to use binomial distribution: discrete
What is the possible range of values can I get, the possible times the events happen
Binomial cant be fractions
E.g. max 10 times, so 0-10 is the range
Gaussian, for continuous distributions, weight, height,
She
7. the times in seconds taken by an athlete to run 400 m on 7 successive days were:
53.2, 55.7, 54.2, 53.6, 59.3, 54, and 53.7
find the mean, median and standard deviation of the times
mean= (53.2+55.7+ 54.2+53.6+59.3+54+ 53.7)/7=54.81
sd=2.132
median=4th
Stat 211 - Tutorial 4 SOlutions/Answers
Questions are adapted from the book titled "A concise course in advanced level statistics: with worked examples" by J. Crawshaw and J. Chambers. 1. (a) 0.2927 (b) 420.40ml 2. A machine is used to fill tubes, of nomi
Stat 211 - Tutorial 4
Questions are adapted from the book titled "A concise course in advanced level statistics: with worked examples" by J. Crawshaw and J. Chambers. 1. (Page 401, Mixed Test 7A, Question 1) A smoker's blood nicotine level, measured in ng
Stat 211 - Tutorial 3 Solution/Answers
1. (a) x -5 5 P (X = x) 25/36 10/36 20 1/36 (b) E(X) = -$1.53 and V ar(X) = 33.08256. x 100 P (X = x) 0.6 200 0.4
2. (a)
2 (b) mean, x = $140; variance, x = 2400; standard deviation, x = $48.99. 2 (c) mean, y = $147;
Stat 211 - Tutorial 3
1. Bart pays $5 to play a game in which he throws two dice. If he gets 2 fives, he wins $25. If he gets only 1 five, he wins $10. Otherwise, he wins nothing. (a) Provide the probability distribution of X, where X represents Bart's pr
Stat 211 - Tutorial 2 Solution/Answers
1. P (A B) = 0.1367 and P (A B) = 0.6133. 2. P (A B) = 0 and P (A B) = 0.75. 3. (a) 0.068608 (b) 0.140 4. Three people A, B and C are playing cards, each being equally likely to win the game. (a) In two consecutive g
Stat 211 - Tutorial 2
1. You are given that A and B are independent events. Additionally, P (A) = 5 P (B) = 16 .Find P (A B) and P (A B).
7 16
and
7 16
2. You are given that A and B are mutually exclusive events. Additionally, P (A) = 5 and P (B) = 16 .Fi
Stat 211 - Tutorial 1 Solutions
1. A closing price (in dollars) at Dec 31, 2011 of 30 stocks in a portfolio are given below: 52.78 55.88 51.12 48.27 40.72 52.39 49.82 51.69 54.59 55.85 47.59 52.48 54.60 57.19 49.04 52.87 54.83 53.34 52.85 50.21 50.49 54.4
Eduardo Martin-Martinez - Math 211 Sec 1
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Second order linear differential equations
1.1
Differential operators
Definition (differential operator). A differential operator L represents a prescribed combination or sequence of operations involving differen