# All Questions

42 questions with bounties
Filter by
Sorted by
Tagged with
187 views
+50

### If You Go Fishing Everyday - What Is The Probability You Know X% Of The Pond?

This is a problem I have recently come across and have been trying to solve it mathematically. Suppose there is a pond with 100 fish Each day, there is a: 5% chance that population of the pond ...
• 3,206
570 views
+50

### Can difference quotient sets be nowhere dense?

Let $f:\mathbb{R} \to \mathbb{R}$ be a function and consider the difference quotient set $$D_f = \left\{\frac{f(y) - f(x)}{y-x} : (x,y) \in \mathbb{R}^2, y > x\right\}$$ Can $D_f$ be nowhere dense ...
297 views
+100

• 2,269
510 views
+100

• 265
175 views
+300

• 129
97 views
+100

84 views
+50

### Probability of Coffee being Hotter than some Temperature?

My cousin and I have been long debating this question: Will a cafe with fresh but inferior quality coffee beans have "better coffee?" compared to a cafe with superior quality coffee beans ...
• 3,206
1 vote
41 views
+50

• 126
73 views
+50

• 823
35 views
+50

### Convergence rate of Laguerre coefficients for polynomially bounded functions

Suppose $f:[0,\infty)\rightarrow\mathbb{R}$ satisfies: $$f(x)= \sum_{n=0}^\infty \hat{f}_n L_n(x),$$ for some $\hat{f}_0,\hat{f}_1,\dots\in\mathbb{R}$, where $L_n$ is the $n$th Laguerre polynomial for ...
• 635
59 views
+150

I am reading Monge's formulation of the optimal transportation problem. It says that one wishes to find the a transport map $T: (X,\mu) \rightarrow (Y,\nu)$ that minimizes the transport cost $$\int_X |... • 129 4 votes 0 answers 43 views +50 ### Characterization of self-conjugate spin^c structures Let M be an oriented Riemannian n-manifold. Then we can choose a trivializing open cover M=\bigcup_\alpha U_\alpha for TM and corresponding transition functions g_{\alpha \beta}:U_\alpha \... • 1,620 0 votes 0 answers 25 views +50 ### Experimental Design: Selecting value of n given desired width of credible interval Suppose I have n IID Bernoulli trials with k successes. Assume that as a prior we are assuming that P(\theta) is uniform on [0,1]. We can pretty easily use Bayes theorem to represent the ... • 3,055 4 votes 1 answer 99 views +50 ### If two Stratonovich SDEs are equal in distribution, do they have the same drifts? General problem: Let X and Y be processes taking values in \mathbb{R}^n which solve the Stratonovich SDEs$$\partial X_t = \sigma(X_t) \partial W_t\partial Y_t = \xi(Y_t) \partial B_t,$$... • 1,042 -3 votes 1 answer 69 views +50 ### Bounding S(n) = \sum_{k=1}^n \mu(k) \left( \pi\left(\frac{n}{k}\right) - \pi(\text{gpf}(k)) \right) I am trying to bound the sum$$S(n) = \sum_{k=1}^n \mu(k) \left( \pi\left(\frac{n}{k}\right) - \pi(\text{gpf}(k)) \right) In other site, I have been given the following "proof". I would ...
• 1,134
Let $f \in L^{p}(\mathbb{R}^{n})$ with $p > \max\{n/2,1\}$. Suppose $u \in L^{2}(\mathbb{R}^{n})$ and let $\{h_{n}\}_{n\in \mathbb{N}}$ be a bounded family of $H^{1}(\mathbb{R}^{n})$ functions ...