I used the following equation but the But the result is not correct : y = k * 10 ^ mx m = slope of line = ∆(log y) / ∆x k = y-intercept: value of y where line crosses the x = 0 axis for example: x0 = 69 x1 = 174 y0 =Read more
I used the following equation but the But the result is not correct : y = k * 10 ^ mx m = slope of line = ∆(log y) / ∆x k = y-intercept: value of y where line crosses the x = 0 axis for example: x0 = 69 x1 = 174 y0 =Read more
Calculate $ $ \int_{C}^{ }\frac{ds}{x^{2}+y^{2}+z^{2}}$ $ Where $ C$ is the first twist of the curve described by $ $ x=\cos(t),y=\sin(t),z=t$ $ I think "the first twist" means the longest interval in which no two points have the same $ x,y$ which happens when $ 0\le t<2\pi$ , so the integral is: $ $ \int_{C}^{Read more
A tourist bridge can only support the mass of 4200kg. We don’t know the pdf of the mass ($ X$ , in kg) of a single tourist. but we do know that $ E(X)=65$ , $ Var(X)=100$ . find good approximation to the probability that the total mass of 64 randomly selected tourists, is moreRead more
In deep learning, such an operation is common: $ $ A = B\circ (C<0.2)$ $ where $ A,B,C\in \mathbb{R}^{n\times m}$ , $ \circ$ denotes Hadamard Multiplication and $ C<0.2$ is the matrix where each element is itself when it is larger than $ 0.2$ and is masked as $ 0$ otherwise. I want to knowRead more
I am stuck at the following exercise: Let $ (X_k)_k$ be a sequence of i.i.d. Bernoulli$ (p)$ distributed RVs with $ p=1/2$ . We want to estimate $ Var(X_1) = p(1-p) = p^2 =: \tau_p^2$ by directly plugging in the natural estimator $ \widetilde{p} := \frac{1}{n}\sum_{i=1}^n X_i$ of $ p$ . We call this estimatorRead more
Suppose $ f_1, f_2, \cdots$ is a collection of measurable functions which satisfy $ \sup_n \int |f_n|^{1 + \gamma}\ d\mu< \infty$ for some $ \gamma > 1$ , and $ \mu$ is a finite measure. I am being asked to show that the $ \{f_n\}$ are uniformly absolutely continuous. That is, for each $ \epsilonRead more
Given a set $ X$ and a closure operator $ \text{cl}:2^X\to 2^X$ on $ X$ , if we define $ \psi:2^X\to 2^X$ s.t. $ \psi(Q)=\{q\in Q:q\in\text{cl}(Q\setminus\{q\})\}$ then is it true that $ \forall S\subseteq X(\psi(\psi(S))=\psi(S))$ (i.e. that $ \psi$ is idempotent) implies $ \text{cl}$ is the closure operator of some matroid? I know if $Read more
I posted this question at MathOverflow, but then I realized that maybe it is more appropriate to ask it here: Let $ f$ be a multiplicative arithmetic function which maps $ \mathbb{N}$ to itself, such as $ \sigma=$ sum of divisors, $ \phi = $ Euler phi-function or $ \tau = $ number of divisors.Read more
Let $ \gamma$ be a limit ordinal with cofinality $ \kappa > \omega$ . Is there a stationary subset of $ \gamma$ (a subset of $ \gamma$ that meets every closed unbounded subset of $ \gamma$ ) of size $ \kappa$ ?Read more
I want to prove or disprove that the Fourier transform $ \mathcal F \colon (\mathcal S(\mathbb R^d), \lVert \cdot \rVert_1) \to L^1(\mathbb R^d)$ is unbounded, where $ \lVert\cdot \rVert_1$ denotes the $ L^1(\mathbb R^d)$ -norm. Having thought about this for a moment, I believe it is indeed unbounded. So I tried to find a sequenceRead more