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Discrete Structures

Mean, Median, Mode and Standard Deviaton

1. Suppose you have administered a test of manual dexterity to two groups of 10 semi-skilled workers. one of these two groups of workers will be employed by you to work in a ware house with many fragile items. the higher the manual dexterity of a worker the less likelyhood that worker wil break significant inventory.Because of a

Product of Disjoint Cycles

In S(5) let pi=(245)(1354)(125). Write pi as a product of disjoint cycles and then answer the following questions. (a) Determine pi^2, pi^5, pi^(-1). (b) What is the order of pi? Why?

Data Distributions and Standard Deviation

In this Unit, you studied several measures of central tendency. By far the most frequently utilized of these measures is the mean of a population. Remember that the source of the data that you want to analyze always comes from what is called a population. If you are interested in the average high temperature in your area for the

Tree Graphs and Minimal Spanning Trees

1.Use the depth-first search numbering obtained in the indicated exercise to list the back edges in the graph. Use the file (5.3jpg) 2. Use Prim's algorithm to find a minimal spanning tree for each weighted graph. (Start at A) Give the weight of the minimal spanning tree found Use 5.2prims.jpg

Bit Strings

(a) How many bit strings of length 6 are there? Explain fully. (b) How many bit strings of length 6 are there which begin with a 0 and end with a 0? Explain fully. (c) How many bit strings of length 6 start with a 0 bit or end with a 0 bit? Explain fully.

Equivalence Relations

H is the relation on the set of all people given by H = {(a,b)|a and b are the same height}. Is H an equivalence relation? Explain your answer.

Discrete Math : Logic (40 MC Problems)

1. Identify the rule of inference used in the following: If it rains today, the flood gates will open. The flood gates did not open today. Therefore, it did not rain. a. modus tollens b. hypothetical syllogism c. modus ponens d. disjunctive syllogism 2. Identify the rule of inference used in the following: If I work all

Merge Sort : splitting and merging trees

Sort the given sequence of numbers using merge sort. Draw the splitting and merging trees for each application of the procedure. -1, 0, 2, -2, 3, 6, -3, 5, 1, 4

Discrete Structures Questions

1. By using the Pigeonhole Principle, we can show that if you take six classes in a term and classes do not meet on the weekend, then at least three of the classes must meet on the same day. True False 2. By using the Pigeonhole Principle, it can be shown that if you are paid bi-weekly (every two weeks) duri

mod-5 and Boolean Functions

1) If f is the mod-5 function, compute each of the following. a) f(17) b) f(48) c) f(169) 3) Convert (1011101)2 to base 16 (i.e., hex) 4) Find the sum of products expansion of this Boolean function F(x,y) that equals 1 if and only if x = 1. Note: one can write out the phrase "y complement" to represent the notation f

A Recursive Definition

(See attached file for full problem description). --- Give a recursive definition of a) the sequence {an}, n=1,2,3,...if i. an = 1+(-1)n ii. an = n2 b) of the set of ordered pairs of positive integers S = {(a,b) | a є Z+, b є Z+, and 3 |(a+b)}.

Standard form

Perform operation and write the result in standard form (5 - 4i) / (3 - 2i)

RSA encryptions

(See attached file for full problem description) --- Consider the RSA encryption system given by p=43,q=59, and e=13 i) Find d such that ed ≡ 1 (mod (p-1)(q-1)) ii) Decode the message : 1552 2069 1178 1637 1975 Using the convention A = 00, B = 01, ..., Z = 25 ---

Common Solutions for Congruences

Find all common solutions to the congruences (in the following notations the = is meant to be a congruence symbol) x=2(mod 3), x=1(mod 4), x=3(mod 5), x=4(mod 7).

Big O notation

I) Show that x^3 is O(x^4) but x^4 is not O(x^3) ii)Show that xlnx is O(x^2) but x^2 is not O(xlnx) iii)Show that a^x O(b^x) but b^x is not O(a^x) if 0 < a < b (0 = zero) iv)Show that 1^k + 2^k+...+n^k is O(n^(k+1)) for every positive integer k

Formula - Several Problems

(See attached file for full problem description with proper symbols) --- 2. Let f(x) = x2 +1 and g(x) = {x+1, x> =3; x-1, x<3 so both f and g map R into Find the formula for a. (f+g)(x) b. (f .g)(x) c. (f o g)(x) d. (g o f)(x) 3. Let A = {a,b,c,d} and B = {1,2,3} and let f : A &#61664; B be a function . Let g : Z

Discrete structures located

We worked on the attached problems today in class I am now trying to work through them again for understanding and I am not getting very far. My skills in discrete mathematics are not such that I can work through these on my own effectively. 3. Seven points are located in a plane. List the possible numbers of lines determi

Bias for a random sample

If we observe a random sample X1...Xn from a distribution with the pdf... Obtain the MLE of mu. Is it unbiased? Please see attached.

Sign and rough magnitude

The plot below is the observed values of two random variables X and Y. What is the sign and a rough magnitude of the Corr (X,Y)? Please see attached.

Discrete Structures : Sequences, Subsequences and Remainders

1. How do I prove that in a group of n people there are two people with the same number of acquaintances within the group? 2. Prove that given a sequence of twelve integers, a1, a2, ...,a12, there is a subsequence aj, aj+1, ..., ak where 12 divides &#8721;kn= aa n. 3. A scrape of paper is found in an old desk that read:

Frequency

When a pair of dice is rolled, the total will range from 2 (1,1) to 12 (6,6). It is a fact that some numbers will occur more frequently than others as the dice are rolled over and over. Why will some numbers come up more frequently than others? Each die has six sides numbered from 1 to 6. How many possible ways can a numb

Suppose that only 25% of all drivers...

48. Suppose that only 25% of all drivers come to a complete stop at an intersection having flashing red lights in all directions when no other cars are visible... (see attachment for complete question)

Handshakes

On the first day of math class, 20 people are present in the room. To become acquainted with one another, each person shakes hands just once with everyone else. How many handshakes take place?

Truth Table Functions Represented

Let p represent some false statement and let q represent some true statement. What is the truth value of each of the following: a. ~(~p v q) b. ~(p v q) c. (~p) v q