Statistics HW 4 solution
14.27
1: Burning time of flare of brand A 2: Burning time of flare of brand B
3: Burning time of flare of brand C 4: Burning time of flare of brand D
(a)
H 0 : 1 2 3 = 4
H 1 : At least two means differ.
Required Conditions:
(1) As
CSE 413, Analysis of Algorithms
Fall Semester, 2004
Assignment 6: Graph Algorithms I
Due Date: Nov. 12, 2004 (at the beginning of CSE 413 class) Note: We assume that all input graphs are based on the adjacency list representation (see page 84 of Manber's
13.43
Define 1 as the average crop yield using the current fertilizer.
Define 2 as the average crop yield using the new fertilizer.
Defile D as ( 2 - 1 )
(a)
H0 : D = 0
H1 : D > 0
Since the population variance (of the difference of the crop yield) is unkn
Homework #1 solutions
Chapter 13
13.7
Define 1 = the average monthly loss when hiring the guard
2 = the average monthly loss when installing cameras
H 0 : ( 1 2 ) = 0
H 1 : ( 1 2 ) < 0
Assume x1 x 2 is normally distributed.
H0 :
=1
H1 :
1
Two-tail F test
CSE 413 Homework 1 Solution Guide 1) For this example, the following path is Hamiltonian. Graphic from: http:/www.cs.sunysb.edu/~algorith/files/hamiltonian-cycle.shtml
2) The Idea: Consider a graph with N vertices. Note that any Hamiltonian Tour must cont
CSE 413, Analysis of Algorithms
Fall Semester, 2004
Assignment 2: Big-O Notation and Recurrence Relations
Due Date: Sept. 17, 2004 (at the beginning of CSE 413 class)
1. Exercise 3.5, page 56.
(20 points)
2. Solve the following recurrence relation. Give a
CSE 413 Homework 2 Solution Guide
Problem 1 a) 100n + log n = Q(n+(log n)^2)
The n term dominates here, and at a large enough n the log n terms are not relevant.
b) log n = Q(log(n2)
log(n2) = 2 log n by the properties of logs So log n <= 2 log n and vice
CSE 413, Analysis of Algorithms Assignment 3: Data Structures
Due Date: Sept. 27, 2004 (at the beginning of CSE 413 class) Note: The problems in this assignment are quite dicult! Please start working on them as early as possible, and ask questions if clar
Homework 3 Solution Guide 1) Idea The important thing to note is that we need to find the kth smallest number in O(klogk) not O(klogn) time. Because of this, we can never perform a remove-min operation on the original binary search tree, because this woul
CSE 413, Analysis of Algorithms
Fall Semester, 2004
Assignment 4: Divide-and-Conquer and Sorting
Due Date: Oct. 8, 2004 (at the beginning of CSE 413 class)
1. For two distinct points p1 = (x1 , y1 ) and p2 = (x2 , y2 ) in the plane, we say that p1 dominat
CSE 413 Homework 4 Solution Guide Problem 1 The points for this problem are not given in sorted order. The algorithm should be O(n log n) time, and it would be convenient to sort the points. Given the desired time complexity, sorting (known to be O(n log
CSE 413, Analysis of Algorithms
Fall Semester, 2004
Assignment 5
Due Date: Nov. 1, 2004 (at the beginning of CSE 413 class)
1. Problem 6.37, page 179. For this problem, the time complexity is not our concern (i.e., your
algorithm may take as much time as
Homework 5 Solution Guide Problem 1 This problem is to find the kth largest element using the minimum space complexity possible. The elements in the list are presented one at a time in some cell C. To find the kth largest element, the largest k elements i
CSE 413 Homework 6 Solutions 1) As a dynamic programming solution, the first step is to determine how the problem depends upon a number of small problems. Consider the problem of finding the path to v using at most i edges. This can be denoted as path(v,i
CSE 413, Analysis of Algorithms
Fall Semester, 2004
Assignment 7: Graph Algorithms II
Due Date: Nov. 24, 2004 (at the beginning of CSE 413 class)
1. The single-source shortest path algorithm discussed in class takes O(|V | + |E|) log |V |) time. That solu
CSE 413 Homework 7 Solutions 1) The general idea is to follow the standard approach for a shortest path, but to consider vertices instead of edges. A heap to find the next smallest path edge based on edges can then be avoided. Start with the source vertex
CSE 413, Analysis of Algorithms
Fall Semester, 2004
Assignment 8: Transformation and NP-hardness
Due Date: Dec. 8, 2004 (at the beginning of CSE 413 class) 1. Consider the following fractional knapsack problem: Given a knapsack of size K and n items of si
Homework 8 Solutions 1) The goal is to fill the knapsack and maximize the total sum of values of the items packed. Because fractions of items can be added, this problem can be solved with a greedy approach. The basic idea is to balance the value of the it
CSE 413, Analysis of Algorithms Assignment 1: The Hamiltonian Cycle Problems
Due Date: Sept. 8, 2004 (at the beginning of CSE 413 class) Fall Semester, 2004
1. Exercise 1.9, page 6 of the textbook. (This is in fact an instance of the Hamiltonian cycle pro
Homework#3
14.3
(a) The detailed calculation is in the excel file.
Source of
variation
Degree of
freedom
Sums of
square
Mean square
Statistic F
Treatments
3
737.8868
245.9623
24.5962
Error
49
490
10
Total
52
1227.8868
(b) The detailed calculation is in th
15.7
Denote pi as the proportion of having outcome i (i = 1 to 5)
H0: p1 = p2 = p3 = p4 = p5 (or p1 = 0.2, p2 = 0.2, p3 = 0.2, p4 = 0.2, and p5 = 0.2)
H1: At least one proportion is not equal to its specified value
Rejection rule: reject H0 if p-value < 0
Homework 6
19.5
(a) (b)
H0: The two population locations are the same.
H1: The location of population 1(new brand) is to the left of the location of
population2 (leading brand)
New
7
8
6
5
4
4
5
4
2
0
0
1
2
3
4
5
Leading
10
8
6
4
2
0
9
7
5
3
1
1
2
0
3
4
5
19.31
Let population 1 be the amount of housework (in hour) wives from two-career families
perform weekly last year.
Let population 2 be the amount of housework (in hour) wives from two-career families
perform weekly this year.
Since the data is interval