Recent content by WMDhamnekar

There was a computation error in my answer to Q.3. ##\frac{V}{4L_1} -\frac{V}{2L_2}= 7 \Rightarrow V\big(\frac{1}{4L_1}- \frac{1}{2L_2}\big)= 7 \Rightarrow \frac{V(L_2-2L_1)}{4L_1L_2} =7 \Rightarrow \frac{7*4L_1L_2}{L_2- 2L_1}= \frac{7*4*1.5*3.5}{3.5-(2*1.5)}= 294 m/s## Hence Author of the...

Relevant video ##\Rightarrow## Physics questions and answers My answer to Q.2 Let's break down the problem and solve it step-by-step: 1. Find the dipole moment (p): The dipole moment is defined as the product of the charge (q) and the separation distance (d) between the charges. p = qd Here...

Where can I ask financial math question in this forum?

My solution: To determine the proportion of time each server is idle in this system, we can use the concept of Markov chains and queueing theory. Here's a step-by-step outline of the approach: 1. Define the States: - Let ( Si) represent the state where server ( i ) is idle. - Since there...

Is it possible to compute the answer using the node 2 (a,c),node 5(a,c,b) node 6(a,c d), node 7 (a,c,e), node 8(a,c,b,d), node 9 (a,c,d,e), node 10(a,c,d,b),node 11(a,c,d e)? Is that answer viable? Note that in this case, we are violating the condition that 'c' should not be before 'b'

I am also a member of www.chemicalforums.com. I visited several times in the last week to this website, but I found the following page instead. When shall I observe these www.chemicalforums.com website again working as usual ?

It is difficult to understand the solution provided in the video to the travelling salesman problem having Hamiltonian circuits with added length constraint. The travelling salesman problem has been solved in the below given video, but I didn't understand lower bound computed for the following...

Can I post Operations research problems in Physics Forum? If yes, where, can I post it?

Problem :Let ##X_0,X_1,\dots,X_n## be independent random variables, each distributed uniformly on [0,1].Find ## E\left[ \min_{1\leq i\leq n}\vert X_0 -X_i\vert \right] ##. Would any member of Physics Forum take efforts to explain with all details the following author's solution to this...

My Answer: The importance sampling identity states that for any measurable function f and random variable X with probability density function p, the expected value of f(X) can be expressed as: ##E[f(X)] = \int f(x) p(x) dx = \int f(x) \frac{p(x)}{q(x)} q(x) dx,## where q is another probability...

Let ##X## be a non-negative random variable and let a > 0. We want to bound the probability ##P\{X \geq a\}## in terms of the moments of X. - Define a function ##h(x) = \mathbb{1}\{x \geq a\}##, where ##\mathbb{1}\{\cdot\}## is the indicator function that returns 1 if the argument is true and 0...

How to use importance sampling identity to obtain the Chernoff bounds as given below? Let X have moment generating function ##\phi(t)= E[e^{tX}]##. Then, for any c > 0 , ##P[X\geq c ]\leq e^{-tc} \phi(t), \text{if t > 0}## ##P[X \leq c]\leq e^{-tc}\phi(t), \text{if t<0} ## Solution...

I cleared my doubt taking suitable guidelines from other statistician on Internet.

My answer: We can proceed as follows. Let ##x \in U_f##. Since ##f## is discontinuous at ##x##, there exists ##\varepsilon > 0## such that for some ##\delta > 0##, we can find ##y, z \in B_{\varepsilon}(x)## with ##d_2(f(y),f(z)) > \delta##. Therefore, ##x \in U^{\delta,\varepsilon}_f##. So...