Assignment 2 Summary
Number of Assignments received: 55
Number of Students in the class (according to spreadsheet): 58 + 1
Marks allocation:
Question
Marks
Criteria
1a
2
1 for each correct answer
1b
2
1 for each correct answer
3
3
1 for
0
1
1
()
2 fo
Summary of Chapter 3: Multivariate Random Variables
Joint C.D.F.
The joint c.d.f. of (X, Y ) is F (x, y) = P (X x, Y y)
Properties of joint c.d.f.
(i) 0 F (x, y) 1 for (x, y) R2
(ii) F (x, y) is non-decreasing in x for fixed y;
F (x, y) is non-decreasin
Summary of Chapter 2: Univariate Random Variables
Random variables
Definition: A random variable X a function from a sample space
S to the set of all real numbers.
The space or range of X is D = cfw_x : x = X(s), s S.
X is a discrete r.v. if D is finit
Summary of Chapter 4: Estimation
Let X = (X1 , , Xn )T be a random sample, that is, X1 , , Xn are i.i.d. random variables from
the distribution with p.m.f. or p.d.f. f (x, ), where = (1 , , k )T are the unknown parameters.
Let x = (x1 , , xn )T be the rea
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Chap 1.2
STAT 330 L. Wang
Thursday, May 14, 2015
Stat330Lectures Page 1
Chap 1.3a
STAT 330 L. Wang
Thursday, May 14, 2015
Stat330Lectures Page 2
Chap 1.3b
STAT 330 L. Wang
Thursday, May 14, 2015
Stat330Lectures Page 3
Chap 1.3c
STAT 330 L. Wang
Thursday,
Summary
Chapter 1: Probability
- Set Theory
- Probability
- Conditional Probability:
Multiplication rule: P (A B) = P (B | A)P (A)
P
Law of total probability: P (B) = ni=1 P (B | Ai )P (Ai )
Bayes Theorem: P (Aj | B) =
P (B|Aj )P (Aj )
Pn
i=1 P (B|Ai )
Assignment 1 Summary
Number of Assignments received: 57
Number of Students in the class (according to CourSys): 58 + 1
Marks allocation:
Question
Marks
Criteria
1
2
0.5 for each correct answer
2
3
1 for P(C)
0.5 for each of the others
3
3
Reasonable proof
STAT 330 Assignment 2
Due: 11:00am, Tuesday, February 21, 2012
Please drop your assignment to the assignment-dropping box. It is
located right beside the statistics workshop, which is one level down
the main oce of Department of Statistics. Please drop be
STAT 330 Assignment 3
Due: 3:00pm, Tuesday, March 6, 2012
Please drop your assignment to the assignment-dropping box.
It is located right beside the statistics workshop, which is one level
down the main oce of Department of Statistics. Please drop
before
STAT 330 Assignment 1
Due: 3:00pm, Thursday, February 2, 2012
1) A positive integer from one to six is to be chosen by casting a die. Thus the
elements c of the sample space C are 1,2,3,4,5,6. Suppose C1 = cfw_1, 2, 3, 4 and
1
C2 = cfw_3, 4, 5, 6. If the
Set Theory
Subset
- A B includes A = B
- If A B and B A, then A = B
Null set
Union OR
Intersection AND
Complement Ac
Difference A B c , Ac B
The laws of sets
1. Demorgans law: (A B)c = Ac B c , (A B)c = Ac B c
2. Associative law: (A B) C = A (B C)
1.
The table below shows, in the column labelled BEFORE, 15
measurements of the speed of sound in air. After taking the
measurements the machine is recalibrated and a further 15
measurements are taken; these are in the column labelled after.
Differences b
Assignment 4 Solutions
1.
Chapter 6 Q 10:
1.
Recall the facts:
and
Then
ch is more than
2.
2.
,
whi
so that
is not an unbiased estimate of
On the other hand
if k=1/n.
which is
Chapter 6 Q 14:
1.
2.
3.
525-202+1 = 324.
This estimate will be right if we hav
1.
2.
3.
1.
Assignment 7
Pregnancy Question: This is a clearly paired data problem so that
the unpaired test is not valid. You use the data step to create a
variable equal to the difference between the two pregnancy glucose
levels. Then proc means provide
1.
2.
The Intelligence Quotient, or IQ, as measured by a certain
psychological test is supposed to have a population distribution
with mean 100 and standard deviation 15. Suppose I suspected that
the mean IQ of children in Vancouver city public schools is
1.
2.
Assignment 1 Solutions
The most obvious source of probable bias is this: teachers are likely
to move economically disadvantaged children to the group getting
free milk. Typically these students will have the most to gain in
educational or nutritiona