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Are these true for a martingale? $Eleft[ frac{X_{n+1}}{X_n} right] = 1, Eleft[ frac{X_{n+2}}{X_n} right] = 1 $

Let $(X_n)_{n in mathbb{Z}_+}$be a martingale, $X_n(omega) neq 0$, and $X_{n+1}/X_n, X_{n+2}/X_n in L^1 (n in mathbb{Z}_+)$ Do the following hold for $n in mathbb{Z}_+$?...

1

Mathematics Asked on 2 years ago

Linear programming: model to only pick 10% of the variables as non zero

I am building a linear programming model. For the sake of simplicity, Imagine that I'm trying to fill a bunch of items into a bunch of boxes. I have a...

1

Mathematics Asked on 2 years ago

Solving vector differential equation

I want to solve the following vector-differential equation for $phi$ in terms of the rest of the variables. $phi = -tau mathbf{v}cdot mathbf{F}+(mathbf{v}timesmathbf{s})cdotnabla_{mathbf{v}}phi$. I am new to vector...

0

Mathematics Asked on 2 years ago

The Optimal Toaster Problem

Suppose I have 3 slices of bread, say $b_1$, $b_2$, $b_3$, and I want each to be double toasted. My toaster has a capacity of 2 slices...

1

Mathematics Asked on 2 years ago

Is it acceptable to run 10-3 wire to a 110V 20A junction box?

I have leftover 10/3 wire from a 220V outlet installation. I need to install a 110V outlet and splice to an existing junction box. Using the existing 10/3 wire will...

6

Home Improvement Asked on 2 years ago

Does dimming preserve the life of LEDs?

I recently installed some decorative LED shelf lighting (specifically these if it makes a difference). The manufacturer says they will last 50,000 hours, where "last" means maintaining...

3

Home Improvement Asked on 2 years ago

Better to run air conditioner fan on high or low speed?

In my apartment, I have two window air conditioning units. Both have different settings for the fan speed: one has two speed options and the other has three. ...

8

Home Improvement Asked on 2 years ago

toilet basin rattling valve

our toilet water basin valve makes a terrible rattling noise when filling up with water. It's the left side tube making that. Any idea about possible solutions beyond calling a...

1

Home Improvement Asked on 2 years ago

Changing a 2way & a 1 way AU light switch to a smart light switch

I have purchased a 1 gang and a 2 gang smart switch with the back as thi 1st picture. The attached are the existing wiring points. Currently the...

1

Home Improvement Asked on 2 years ago

How does a Smart Switch that does not require a neutral work?

I read on the internet that a Smart Switch that does not require a neutral works via a hub because that's where it stores the credentials to the wireless network....

1

Home Improvement Asked on 2 years ago

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