One can also think of probability generating functions as (flipped) Z transforms, moment generating functions as (flipped Laplace transforms), and characteristic functions as Fourier transforms of the respective PMF/PDF. Lot of their properties then follow from simple properties of Signals and Systems.
Don't have a reference on the top of my head, but the main idea is as follows:
The definition of MGF of a random variable with PDF f(x) is
E[e^{sX}] = int_{-inf}^{inf} f(x) e^{sx} dx
The definition of Laplace Transform of a signal f(t) is
F(s) = int _{-inf}^{inf} f(t) e^{-st} dt
Hence MGF is 'flipped' Laplace transform
Now for we know that the MGF of sum independent RVs is the product of their MGFs. So if we take the inverse Laplace transform, the density of the sum is convolution of the individual densities.
Similarly, if we take derivative in frequency domain, that is same as multiplying in time domain: So M'_X(s) is the 'flipped Laplace transform' of x f(x) and its value at s=0 is the 'DC-gain' of the signal.
And so on... the properties are all immediate consequence of the definition of MGF and since the definition is essentially the same as that of a Laplace transform , there is an equivalent property in signals and systems as well.
From the little I know about ML in general, you always want to introduce randomness so you don't get stuck in a local minimum/maximum. So they're all risk seeking?
This is magnified 2x (to show the similarity). Both the sample alphabet and the "character differences" shows uppercase-eye and lowercase-ell as the identical glyph, for DPSansMono.
You are putting together a compelling argument for both skepticism and caution before placing an order for merchandise from the goodereader store. (not something I planned to do)
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How do you feel about their youtube channel where they review all the various devices in this market segment?
Specifically, have you ever found their reviews to be inaccurate?
Do you know of any alternative source of reviews in this market segment that is as comprehensive or experienced?
One thing I'll say in favor is that they do send their writing staff to the various trade shows.
It will be fascinating if there were a way for you to record the actual time when you do eat lunch (without the time being revealed to you; say a Rasberry Pi where you press a switch to record current time but it has no display). I am curious how much our body clock synchronizes with real time. I see that in my kids, who don't yet know how to read time. But they are hungry right at noon and 7pm, and will get cranky if they don't get something to eat within 15 min of that. Do adults retain such strong internal body clocks?
> "I am curious how much our body clock synchronizes with real time"
Various experiments have been performed with people in caves, where they don't have "time cues" such as natural daylight. From the Michel Siffre wikipedia entry[0]: "He found that without time cues, several people including himself adjusted to a 48-hour rather than a 24-hour cycle ... Several astronauts reported experiences similar to those experienced in underground experiments such as loss of short-term memory to being isolated from external time references." And for Stefania Follini[1]: "her biological clock drifted away from its regular rhythm to following first a 28-hour day, and later on a 48-hour one ... When she finally emerged from the cave at the experiment's end ... she estimated that it was ... only two months from the start of the experiment instead of the four that had actually transpired".
I understand the desire to use Markdown - if you’re not using an editor that will dump the “begin/end” for you with a keystroke or two it feels faster.
The SVG output is written to a local file. KeenWrite converts Markdown to XHTML (XML), which references the local file. ConTeXt then typesets the XML, importing the local vector graphics file and formats it according to the setups defined by the theme.
Kroki has other text-based formats for flow charts, Gantt charts, UML diagrams, packet diagrams, network diagrams, etc.
To be concrete, create a file named "example.md":
Mind Map:
``` diagram-plantuml
@startmindmap
skinparam monochrome true
+ OS
++ Ubuntu
+++ Linux Mint
+++ Kubuntu
+++ Lubuntu
+++ KDE Neon
++ LMDE
++ SolydXK
++ SteamOS
++ Raspbian
-- Windows 95
-- Windows 98
-- Windows NT
--- Windows 8
--- Windows 10
@endmindmap
```
Yes, I can do that– the main change is just the amount of space available for the toolbar. Just mention it in the order form and I'll follow up with a custom build
