Victoria Robinson
Intro to Statistics
October 6, 2015
Probability HW 5.1-5.2
5.1 Exercises
5.1
a) P(survival) = 0.01. About 1% of people who go into cardiac arrest in NYC will survive.
b) According to
Chapter 16 Solutions
This chapter uses computationally demanding resampling procedures for which the use of a
computer is critical. We used S-PLUS while writing this chapter, and give commands below f
Chapter 12 Solutions
12.1. (a) H0 says the population means are all equal. (b) Experiments are best for establishing
causation. (c) ANOVA is used when the explanatory variable has two or more values.
Chapter 15 Solutions
15.1. The rankings are shown on the right. Group A ranks are 1, 2,
4, 6, and 8; Group B ranks are 3, 5, 7, 9, and 10.
Group
A
A
B
A
B
A
B
A
B
B
Rooms
30
68
240
243
329
448
540
552
Chapter 13 Solutions
13.1. (a) Two-way ANOVA is used when there are two explanatory variables. (b) Each
level of A should occur with all three levels of B. (c) The RESIDUAL part of the model
represent
Chapter 17 Solutions
17.4. Possible examples of special causes might include: wind speed and direction, trafc,
temperature, Jeannines health, or mechanical problems with the bicycle (a at tire or a
br
Math 215 Spring 2015
Problem Set 6 Solutions
1. (a) Find an example of some u R2 so that Span(u) is the solution set of the
equation 4x 7y = 0.
Algebraically, the solution set of the equation 4x 7y =
Math 215 Spring 2015
Problem Set 5 Solutions
1. Dene a function f : cfw_1, 2, 3, 4, . . . , 12 N by letting f (n) be the number of positive
divisors of n. So f (4) = 3 since the divisors of 4 are cfw_
Math 215 Spring 2015
Problem Set 4 Solutions
1. (5 points) For this problem we will do a double containment proof to show the two
sets A = cfw_3x + 1 : x R and B = cfw_3x 2 : x R are equal. Like on th
Math 215 Spring 2015
Problem Set 1 Solutions
1. (6 points) Write each of the lines described below as a set cfw_c v + w : c is in R (i.e.
ll in v and w in the set notation above).
2
(a) The line thr
Math 215 Spring 2015
Problem Set 2 Solutions
1. Negate the following statements. You do not need to prove or disprove the statements, simply write the negation so that no not appears.
(a) For all x R,
Math 215 Spring 2015
Problem Set 13 Solutions
1. Suppose T : R2 R2 is the linear transformation with [T ] =
and u2 =
2
0
2 1
. Let u1 =
5 2
1
3
.
(a) Prove that Span(u1 , u2 ) = R2 .
Recall from Theor
Math 215 Spring 2015
Problem Set 15 Solutions
3 1
diagonalizable? If so, nd
1 1
some basis = (u1 , u2 ) so that [T ] is a diagonal matrix.
1. Is the transformation T : R2 R2 with [T ] =
No. Refer back
Math 215 Spring 2015
Problem Set 10 Solutions
1. (a) Write the standard matrix for the transformation which represents projection
onto the line y = 2x.
1
2
Here w =
. So we apply the formula for [Pw ]
Math 215 Spring 2015
Problem Set 9
Due: February 23, 2015
Make sure you are familiar with the Academic Honesty policies for this class, as detailed on the
syllabus. All work is due on the given day by
Math 215 Spring 2015
Problem Set 12 Solutions
1. Determine Null(Pw ) where w =
1
1
. (Recall Pw is projection onto the vector w.)
The Null space is all vectors v so that Pw (v) = 0. Consider an arbitr
Math 215
Linear Algebra
Spring 2011
Lectures
Jan. 24
Systems of linear equations; matrix reduction (1.1)
Jan. 26
Row reduction; echelon forms (1.2)
Jan. 28
Vectors in Rn; relationship to systems of eq