/sci/ - Science & Math

>>14873836
(Math repost 2)
>reposting for math
Where [math] Z [/math] is called the [math] Z [/math]-value and is calculated as follows [eqn] Z = \frac{\mu - \mu_0}{\sigma / \sqrt{n}} [/eqn]Where [math] \mu [/math] is the average you got (in this case 56.1), [math] \mu_0 [/math] is the hypothesized or expected average (in this case 49.5), [math] n [/math] is the number of random numbers you generated and [math] \sigma [/math] is the standard deviation of your sampling distribution. For a discrete uniform distribution the standard deviation will be [eqn] \sigma = \sqrt{ \frac{m^2-1}{12} } [/eqn]Where [math] m [/math] is the number of elements of the set from which you're choosing random numbers, for the case of generating numbers between 0 and 99 then [math] m [/math] will be 100, if you're generating numbers between 0 and 999 then [math] m [/math] will be 1000, etc.

So i'm going to put all what i just above together to give you an example how you calculate such a probability in practice, first assume we have generated a 1000 numbers between 0 and 99, now start by calculating the standard deviation, then use it to calculate the [math] Z [/math]-value
[eqn] \sigma = \sqrt{ \frac{100^2-1}{12} } \approx 28.866 [/eqn]
[eqn] Z = \frac{56.1 - 49.5}{28.866 / \sqrt{1000}} \approx 7.230 [/eqn]
So now we can use this to calculate the value of the integral
[eqn] \frac{1}{\sqrt{2\pi}} \int_{7.230}^{\infty} e^{-t^2/2} \; dt \approx 2.414 \cdot 10^{-13} [/eqn]
This probability is EXTREMELY LOW! therefore it provides strong evidence that psychic meddling is real, and in fact such a value would be more anamolous if our [math] n [/math] was larger.

It's very difficult to explain where the math above comes, if you want to understand where these formulas come from then you need to study statistics. For a youtube channel on statistics i only know https://www.youtube.com/user/jbstatistics/videos

(2/2)

>>14856505
Any computation which can be done can be done with a Maid Library. Maid Libraries might be an alternative to Abstract Syntax Trees.