Discrete Definition and 829 Threads

Homework Statement Homework Equations The Attempt at a Solution I'm not really sure if this belongs here or in the precalculus mathematics section. I had to take calculus before taking this class so I'm putting it here. I'm confused about part (b). I don't really...

Solve for x: 4x=6(mod 5) Here is my solution: From the definition of modulus, we can write the above as \frac{4x−6}{5}=k, where k is the remainder resulting from 4x~mod~5=6~mod~5=k. Solving for x, x=\frac{5k+6}{4}⟹x(k)=\frac{5k+6}{4} Now, my teacher said that is incorrect, and that...

The discrete-time spectrum of a sampled continuous-time signal x(t) is shown in the figure above, where (A = 9.8exp(-j0.06π), B = 0.51π, C = -0.27π, and D = 1.9exp(-j0.41π) ). If the sampling frequency is 4928, which of the following continous-time signals is a possible solution for x(t)...

Find the DTFT of: h[n]=(-1)^{n}\frac{sin(\frac{\pi}{2}n}{sin(\pi n} useful properties: x[n]y[n] --> X[Ω]*Y[Ω] \frac{sin(\frac{\pi}{2}n}{sin(\pi n} --> rect[\frac{2Ω}{\pi} I have no clue how to deal with the (-1)[itex]^{n}[\itex] the DTFT of that doesn't converge. . . any help...

Given that GCD(na,nb) = n * GCD(a,b) for a,b,n ∈ Z+ a) Prove that, if GCD(a,b) = 1 then GCD(a+b, a-b) = 1 or GCD(a+b,a-b) = 2 Hint: Let D = GCD(a+b, a-b), show that D | 2a and D | 2b thus D | GCD(2a,2b) then use the given b) Prove that, if GCD(a,B) = 1, then GCD(2a+b, a+2b) = 1 or GCD(2a+b...

Hello guys, I will be taking Linear Algebra (Intro.) and Discrete Math in the Fall. I heard that these two courses are different from the Calculus sequence. I am afraid since I am not good with proofs. Will I be able to do well as long as I put in the time? Can you guys give me an advice so I...

Say I have a model, y = f(x), and ten discrete data points to compare to this model, (x1, y1)...(x10,y10). The normal way would then be to take the residuals and square them to get a quality of fit, ie. average residuals squared = {[f(x1) - y1]^2 + ... + [f(x10) - y10]^2}/10 I also remember...

I can't seem to wrap my head around the types of sums used in probability theory, and here is a classic example. Section 6.1 of this article: http://en.wikipedia.org/wiki/Expected_value#Discrete_distribution_taking_only_non-negative_integer_values The first line of the proof, what is going...

Is there a way to know one way or another? If smallest possible scale is Planck scale, does it mean that space-time is discrete where smallest possible step is Planck's length (PL) and smallest possible time is Planck's time (PT)? If I move my hand from point A to point B, say 1m exactly in...

Hi, I am learning Fourier transformation by my own. I am reading a book "Fourier Transformation" by R. Bracewell. In chapter 11, in examples of discrete Fourier transforms, it gives for N =2, {1 0} transforms to 1/2{1 1}. I can do this in MATLAB but I can't figure it out how to do it by hand...

Well I was reading this " A Mathematical Theory of Communication" paper by Claude Shannon. He says that the capacity of a discrete channel is given by [ tex ] C= \ \lim_{T \to +\infty} \ \frac{\log ( N(T) )} {T} [ \tex ] Here N(T) is the number of possible sequences in a duration of T...

Consider an unbounded self-adjoint operator defined in a hilbert space(its domain isn't the entire hilbert space,of course).Can its spectrum have discrete and continuous parts simultaneity?Does it have eigenvectors with finite norm? Thanks

Hello, I'm working with a 2 x 3D arrays of fluid velocity values (east-west -> u and north-south -> v) and would like to properly calculate vertical velocities (w) from them (n.b. this is not homework). This ultimately needs to go into a processing algorithm, so while symbolic math is...

How would you go about convolving two discrete distributions that look something like this: Number: 0, 1, 2 Probability: 0.1, 0.3, 0.6 Number: 0, 1, 2, 3, 4 Probability: 0.1, 0.3, 0.2, 0.1, 0.3

Homework Statement If A is a subspace of X and A has discrete topology does X have discrete topolgy?Also if X has discrete topology then does it imply that A must have discrete topology? The Attempt at a Solution My understanding of discrete topology suggests to me that if A is discrete it...

Homework Statement An eletron is moving along one axis between x=0 and x=L. It's mass is given by m. We want to know the energy and wave function of its possible states given by the quantic number n. Show that the solution to the above equation is En=n^2*h^2/(8*m*L^2)...

Homework Statement A certain manufacture advertises batteries that will run under a 75 amp discharge test for an average of 100 minutes, with standard deviation of 5 minutes. a. find an interval that must contain at least 90% of the performance periods fr batteries of this type. b...

...outside integrated circuits? Can OpAmp's replace them?

Homework Statement There are 8 beads: 4 black, 3 white, and 1 red. How many ways can these be arranged on necklace? Homework Equations Just combinations nCm = (n-m)!/(m!). The Attempt at a Solution 8C4 = 70, 4C3 = 24, and 1C1 = 1, so the total number of combinations is 95? Or...

Hello, I am trying to quantify the difference between two discrete distributions. I have been reading online and there seems to be a few different ways such as a Kolmogorov-Smirnov test and a chi squared test. My first question is which of these is the correct method for comparing the...

Homework Statement 9. This is a simplified inventory problem.Suppose that it costs c dollars to stock an item and that the item sells for s dollars. Suppose that the number of items that will be asked for by customers is a random variable with the frequency function p(k). Find a rule for...

Homework Statement Homework Equations a. I know that x*a mod y should be the same as y*b mod x but I don't understand why b. I know that an inverse can be constructed because x and y are mutually prime and gcd(x,y) = 1 , but I have no clue at what pair x and m is possible c. I have no idea...

Hi all, I'm reading the following PDF about the DFT: http://www.analog.com/static/imported-files/tech_docs/dsp_book_Ch8.pdf Please see pages 152-153. So the inverse DFT (frequency to space, x[i] = ...) is given on page 152. Then it is claimed that the amplitudes for the space-domain...

Discrete signal x[n] is shown in the first picture. Sketch x[2n] Answer Can anyone ecplain why x[2n] is like that. I can understand how to plot it if i have a continuous time signal

See attachment for the question. ---------------- ∀x ∈ D, if P(x) then Q(x). this means ∀x P(x) -> Q(x). all you have to do is find a value for x ∀x this means for ALL x right so you can choose ANY element but for the E its only things in the domain so all you have to do is choose an x...

Homework Statement The textbook exercise asks for a Hausdorff topology on \{a,b,c,d,e\} which is not the discrete topology (the power set). It is from "Introduction to Topology, Pure and Applied", by Adams and Franzosa. Homework Equations Let X be a set. Definition of topology...

Hi members of the forum, Please consider the following: Given $\displaystyle a_{n}=\frac{n^2+1}{\sqrt{n^2+4}}$ where $\displaystyle n\in\mathbb{N}$ and $\displaystyle b_n=\prod_{k=1}^n(a_k)$ prove that $\displaystyle \frac{b_{n}}{\sqrt{2}}=\frac{\sqrt{n^2+1}}{\sqrt{n^2+2n+2}}$. Therefore...

In the page that I attached, it says "...while at the continuity points x of F_x (i.e., x \not= 0), lim F_{X_n}(x) = F_X(x)." But we know that the graph of F_X(x) is a straight line y=0, with only x=0 at y=1, right? But then all the points to the right of zero should not be equal to the limit of...

The DCT of an even function is comprised of just cosine coefficients, correct? I'm playing around in MATLAB and I came up with a simple even function 1.0000 0.7500 0.5000 0.2500 0 0.2500 0.5000 0.7500 1.0000 0.7500 0.5000 0.2500 0 0 0 0...

Hello all. I have a homework question but since I have no idea how to go about solving it I have started with an exercise problem from the book (with the solution and vague steps provided). Here is my attempt of the exersize question. Homework Statement Compute the convolution y[n] = x[n]...

Homework Statement A binary information source produces 0 and 1 with equal probability. The output of the source, denoted as X, is transmitted via an additive white Gaussian noise (AWGN) channel. The output of the channel, denoted as Y, satisfies Y = X + N, where the random noise N has the...

Homework Statement http://puu.sh/1OfE2 Homework Equations The Attempt at a Solution I am not really sure about this one! :( I think it's 1 because http://puu.sh/1OfY0 http://puu.sh/1OfYE I came up the number by working backwards (assuming the conclusion is true). However, for a proof, I...

I am new to manifolds and I read the fact that any discrete space is a 0 dimensional manifold. I am having a hard time understanding why and feel this is very basic. So to be a manifold, each point in the space should have a neighborhood about it that is homeomorphic to R^n. (and n will...

Hi, I'm trying to simulate a discrete time time markov chain in matlab. Unfortunately I am neither a markov chain expert or a good MATLAB coder. My problem is simple, I have a transition probability matrix with 100 states (100x100) and I want to simulate a 1000 steps beginning from state 1...

Why does a discrete Fourier transform seems to produce two peaks for a single sine wave? It seems to be the case that the spectrum ends halfway through the transform and then reappears as a mirror image; why is that? And what is the use of this mirror image? If I want to recover the frequency...

[FONT=Courier]Classify the following as discrete or continuous random variables. [FONT=Courier] [FONT=Courier](A) The number of people in India [FONT=Courier](B) The time it takes to overhaul an engine [FONT=Courier](C) The blood pressures of patients admitted to a hospital in one day...

Homework Statement is there a continuous real valued variable X with mgf: (1/2)(1+e^t) Homework Equations The Attempt at a Solution I've noticed that this is the mgf of a bernoulli distribution with p =1/2. But since bernoulli is a discrete distribution, does that disprove that...

I've been trying to figure out why it's standard to use complex discrete Fourier transforms instead of just the real version. It's discussed a bit here. http://dsp.stackexchange.com/questions/1406/real-discrete-fourier-transform As far as I can tell there's a hypothetical efficiency...

I'm having difficulties trying to establish the best approach to create a mathematical model of a process that has a combined continuous and discrete (batch) element to it. I explain as follows: The system is a hopper (vessel), open to atmosphere, with dry granular material being fed in by...

Hi, If X \LARGE is a metric space and E \subset X is a discrete set then is E \LARGE open or closed or both? Here's my understanding: E \LARGE is closed relative to X \LARGE. proof: If p \subset E then by definition p \LARGE is an isolated point of E \LARGE, which implies that p...

Hello, You can use a Q-Q plot to visually test if 2 continuous variables are from the same distribution and you get a straight line. Is there a way to visually test if 2 discrete variables are from the same distribution? Also is there a way to test it mathematically? Thanks

Homework Statement Let \theta \in [0,1] and n \in \mathbb{Z} . Let n\theta mod(1) denote n\theta minus the integer part. Show n \theta mod(1) is a discrete subset of [0,1] if and only if theta is rational.The Attempt at a Solution I'm having a bit of trouble with the "only if" part...

Here is the question: Consider the experiment of rolling two tetrahedra that are unfair in the sense that each has the following probabilities for each of the four faces: P{1 dot}=1/10 P{2 dots}=2/10 P{3 dots}=3/10 P{4 dots}=4/10 Let X be the total of the outcomes in the two...

Say you have some function that is periodic in a parameter k. The discrete Fourier transform from a sampling may be found in the usual way, giving the frequency spectrum in k. But what if I want to find the frequency spectrum in 1/k ? I'm not really sure what this is called, and so I've had a...

I have a grid and on each point on the grid I have discrete velocity data. I however don't have anyalytical function. I need to integrate the points and check where in space they will be after some time. I know it very easy to do it with runge-kutta if i have the analytical function for velocity...

Hi, I have 3 correlated variables that I wish to model with a copula function. 2 of the variables are continuous and 1 is discrete. My question is, generally speaking can you model continuous and discrete variables within the same copula? Yes/No? Thanks

Hi, So I am trying to show the following: ##(A \cup B)\sqcup(A \cap B) \leftrightarrow A \sqcup B## The proof that I am trying to understand starts with: ##A \leftrightarrow (A \backslash B) \sqcup (A\cup B) \qquad (1)##, and ##A \cup B \leftrightarrow (A\backslash B)\sqcup B \qquad...

Homework Statement I'm having trouble understanding PMF. We are given a number, say, 927189234. We need to calculate the PMF of (0, 1, ..., 9) in this distribution. Homework Equations The Attempt at a Solution Calculating the probabilities is easy, P(9) = 2/9 P(8) = 1/9...

Homework Statement Find the Impulse response of this system 3y[n]+4y[n-1]+y[n-2] = x[n] + x[n-1] Homework Equations Eigenvalues = -1/3 and -1 hc[n] = k1[-1/3]n+k2[-1]n 3h[n] +4h[n-1] +h[n-2] = δ[n] + δ[n+1] The Attempt at a Solution I know that normally we would plug in hc[n] for two...

Hello, This semester I am taking my first discrete math course. I am thoroughly enjoying the material, but am dreading the professor and textbook. The consensus amongst my classmates is that the professor is excessively convoluted in his conveyance of the material, and that the textbook does...