Discrete Definition and 829 Threads

Homework Statement A fair coin has a ##1## painted upon one side and a ##2## painted upon the other side. The coin is tossed ##3## times. Write down a sample space for this experiment. Let ##X_1## be the sum of the numbers obtained on the first ##2## tosses and ##X_2## be the sum of the numbers...

Homework Statement Find the probability that a randomly generated bit string of length 10 begins with a 1 or ends with a 00 if a)a 0 bit and a 1 bit are equally likely. b)The probability that a bit is a 1 is .7 c)The probability that the ith bit is a 1 is 1/2i for i=1,2,3,...,10 Homework...

Okay, my online class has posed another word problem and I cannot seem to understand this week's material or how to formulate a solution. Here it is: Imagine you are in a game show, a money give-away! There are 4 prizes hidden on a game board with 16 spaces. One prize is worth \$4000...

$$ƒ = b^n$$ $$ b,n,I ∈ ℤ $$ Condition: Upon choosing a base value b.. $$ n | b^n ≤ I $$ (n is determined based off the value of b to yield the highest ƒ without going over I) $$1<b<L , L<<I$$ where I is some large number, and L is also sufficiently large such that we want to avoid going...

Good day to you all, First, I want to let you all know that I'm new at this and that my question could be a bit vague so I'll try and do my best to explain what I want to know. I read on a forum about the Hubble's value decreasing over time despite the fact that the expansion of the Universe...

Homework Statement Suppose we have a discrete random variable whose values $X = x$ can include the value $0$. Some examples are: ##X\sim \text{Binomial}(n,p)## with ##x = 0,1,2,\ldots,n## and ##X\sim \text{Poisson}(\lambda)## with ##x = 0,1,2,3,\ldots## Sometimes we can only observe these...

We know that in the continuous math, e is special number because if f(x) = e^x, so f'(x) = f(x). But in discrete math, what's the constante base that satisfies this condition? Is not the 2? I. e. f(n) = 2^n ? Thanks,

I'm trying to calculate this limit to answer a question in Quantum Mechanics: \mathop {\lim }\limits_{{t_1} \to 0} \,\,{\left( {\frac{m}{{2\pi \hbar i{t_1}}}} \right)^{{\raise0.5ex\hbox{$\scriptstyle 1$} \kern-0.1em/\kern-0.15em \lower0.25ex\hbox{$\scriptstyle 2$}}}}{e^{im{{(x' - x)}^2}/2\hbar...

Homework Statement We ask a person to taste 18 biscuits , 8 made to butter ( the other 10 are made to margarine ) , and to identify 8 butter cookies . He does not know the exact number of butter cookies . As he sees no difference , he randomly selects those he claims to be butter . Y = the...

Homework Statement Find ##x[n] \ast h[n]## when ##x[n] = 3 u[2-n]## and ##h[n] = 4\left( \frac{1}{2} \right)^{n+2}u[n+4]## where ##u[n-k]## is the unit step function. Homework Equations None really The Attempt at a Solution So I know this is probably simple but I am confused. So the...

Hi everyone, I'm helping my professor pick out a new Discrete math book. He has been using Discrete Mathematical Structures 6th Kolman for at least 4+ years. He's on the search of finding one, but hasn't been successful with it. I was wondering what kind of textbook you would recommend. I will...

Hello all I have this question I am trying to solve. In an urn there are 6 balls, numbered: 1,2,3,4,5,6. We take 4 balls outs, without replacement. X - the minimal number we see Y - the maximal number we see I need to joint distribution. I understand that X is getting the values 1,2,3 while...

Can someone help me solve this problem I need to Define the following relation on the set of real numbers xRy if |x - y| is an even integer and Show that R is an equivalence relation and describe the equivalence classes.

For the life of me I am having a hard time understanding how to do problems of this nature. As I understand it, were using the multiplication rule here with a twist.a. How many integers from 1 through 100,000 contain the digit 6 exactly once? 5 * 9 * 9 * 9 * 9 = 38805 is what I have. Because...

Hello,*please refer to the table above. I started from x(n)=x(n*Ts)=x(t)*delta(t-nTs), how can we have finite terms for discrete time F.S can anyone provide me a derivation or proof for Discrete F.S.?

Consider a set X with |X|=n≥1 elements. A family F of distinct subsets of X is sad to have property P if there exist A and B in F, such that A is a proper subset of B and |B\A|=1. Determine the least value m, so that any F with |F|>m has property P. This is a problem asked by our Discrete...

Homework Statement My task is to find out what is the lowest # of elements a poset can have with the following characteristics. If such a set exists I should show it and if it doesn't I must prove it. 1) has infimum of all its subsets, but there is a subset with no supremum 2) has two maximal...

One hundred pennies are being distributed independently and at random into 30 boxes, labeled 1, 2, ..., 30. What is the probability that there are exactly 3 pennies in box number 1? I tried using a Poisson distribution f(x) = (e^-λ)*(λ^x)/x! , with λ = 100/30 = 10/3 and x = 3. I got 0.22021 (5...

I study a textbook in Discrete Math 7e Rosen , I am in ch.4 Number Theory Mainly for computer science improvement (cs) Is it ok study same time a Probability & Statistics textbook again for cs...? I have background in Calculus I II and Linear Algebra & web development.

In my circuits/active devices course we had to make amplifier designs with various type of transistors (BJT, JFET, MOSFET). In each design the transistor beta parameter played an important role in deciding which resistors to use in the final amplifier circuit. This beta parameter changes widely...

Hi all, Due to a scheduling conflict at my university I can't take Discrete Math, and it's a pre-requisite for all of the math courses I want to take next year. Any recommendations on which textbooks I ought to use to independently study the subject? Thanks!

Homework Statement [/B] Sorry that I wasn't able to fit everything in the title. I got 2/3 on this on my quiz, and am wondering what I did wrong, or could have done better. Thanks in advance. Show that if A ⊆ B and C ⊆ D, then A X C ⊆ B X D Homework Equations The Attempt at a Solution For a...

Homework Statement 1. Consider selecting at random a student who is among the 15,000 registered for the current semester at a school Let X be the number of courses for which the selected student is registered and suppose that X has probability distribution x: 1 2 3 4 5 6...

I am a little confused of the last step. We can set an upper boundary for any arbitrary large number M, so it seems ok. do you agree on the last statement?

I have multiple problems in the current homework set that say something along the lines of "try to define a function f: S -> S by the rule f(n) = n^2 for each n in S. Then it asks a couple questions such as "is the function well defined" or "is it one-to-one/onto" I'm just confused on what its...

Hi I am trying to program excel to take the DFT of a signal, then bring it back to the time domain after a low pass filter. I have a code that can handle simple data for example t = [ 0, 1, 2, 3] y = [2, 3, -1, 4] So I think everything is great and so I plug in my real signal and things go off...

Hello! Can you give me information about the subject Discrete Geometry? What is it about? What knowledge is required? (Thinking)

Homework Statement Translate: A, but not both B and C Homework Equations AB = A and B A+B = A or B ~ = not The Attempt at a Solution I'm not sure if my translation of this is correct: A(B XOR C) The statement is throwing off my translation because usually when I use XOR, it means B or C, but...

If there a finite field where both group structures have hard discrete logs? Discrete log in the additive group means multiplicative inverse.

Hi all, Not sure if this would be the right place for this question, but I know it bothers me for some time already and would really appreciate any kind of help. I am trying to fit an HMM, but here for every observation in the sequence I have feature vector - probability distribution that given...

(I guess you could put this in a computer science section since discrete math is the math of computers.) What learning resources do you recommend for learning discrete math from a person who knows none of it to a person who can do it easily? I have tried to study the topics below but the symbols...

(I guess you could put this in a computer science section since discrete math is the math of computers.) What learning resources do you recommend for learning discrete math from a person who knows none of it to a person who can do it easily? I have tried to study the topics below but the symbols...

it is said that the energy spectrum of two body and three body decay is discrete and continuous respectively.

(1) For a real function, g(x), the Fourier integral transform is defined by g(x) = \int_{0}^{\infty} A(\omega )cos(2\pi \omega x)d\omega - \int_{0}^{\infty} B(\omega )sin(2\pi \omega x)d\omega where A(\omega ) = 2 \int_{-\infty}^{\infty} g(x)cos(2\pi \omega x)dx and B(\omega ) = 2...

Homework Statement http://ocw.mit.edu/courses/electrical-engineering-and-computer-science/6-003-signals-and-systems-fall-2011/assignments/MIT6_003F11_sol01.pdf [/B] Homework Equations None[/B] The Attempt at a Solution To be honest, I don't think you can prove something is impossible...

what is difference discrete and digital signal

haruspex submitted a new PF Insights post Frequently Made Errors in Probability - Continuous and Discrete Distributions Continue reading the Original PF Insights Post.

Hi, I have an idea which when tested looks like its clearly flawed. I am hoping someone can tell me where my procedure is flawed, or point me to some other theory that has already done something similar. The first two are the laplace transform. The third line is the Fourier Transform. The...

I have some questions related to how a discrete control system is designed. One method is to design the controller in the continuous time domain, arriving at a transfer function (in the s-domain). After that, a transfer function for the ADC system must be taken into consideration. I will suppose...

Hi, I want to transform a complex exponential with quadratic phase to discrete form, in other words to a vector form. can anyone help me with that? Thanks

Does QM contain both discrete particles and fields? If so, why aren't these two mutually exclusive? It seems like one is chunky and the other continuous.

Homework Statement Hey guys I am having a bit of a difficult time with this question, if some one could help me out it would be appreciated, thanks. Consider the following argument. "If the weather is fine, and the train is early, then the dog will sit on the tuckerbox. The train will be...

Is zero discrete?

How do I solve this 1. (a) Solve the recurrence relation an =6an−2 +8an−3 +3an−4 +64·3^n−4, n􏰀>=4 where a0 =0,a1 =1,a2 =4 and a3 =33. (b) Write down a closed form of the generating function of the sequence an.

Homework Statement Let A = {1, 2, 3, 4} and let F be the set of all functions from A to A. Let R be the relation on F defined by: For all functions f, g that are elements of F, (f, g) are only elements of R if and only if f(i) = g(i) for some i that is an element of A. Let the functions α, β...

Hello everyone, I have a discrete class D project that I need help with but since I'm not an analog guy I got a problem. So far I got everything set up and the discrete class D works perfectly. But only at maximum of 6 volts otherwise the Transistor M3 gets really hot and burned, how do I solve...

Hey I am trying to evaluate d/dx, d/dy and d/dz of a wavefunction defined on a grid. I have the wavefunction defined on equally spaced points along three axes a=x+y-z, b=x-y+z and c=-x+y+z. I can therefore construct the derivative matrices d/da, d/db and d/dc using finite differences but I...

Homework Statement my function: sin\frac{N\pi}{2} , N = 1, 2, 3, ... N = 1 ---> f(N) = 1 N = 2 ---> f(N) = 0 N = 3 ---> f(N) = -1 Homework EquationsThe Attempt at a Solution -\frac{1}{2}(-1)^N obviously it's wrong but just an 'attempt' my book refers to the...

Hi, I'm trying to program an arduino to generate a Trapezoidal Motion Profile to control a DC motor with a quadrature encoder. Essentially, the user will input the desired Target Position, Max Velocity and Acceleration (decel = -accel) and the code will calculate the target position versus...

Homework Statement Given a positive integer n written in decimal form, the alternating sum of the digits of n is obtained by starting with the right-most digit, subtracting the digit immediately to its left, adding the next digit to the left, subtracting the next digit and so forth. For...