Thanks so much bpet, I believe your solution above solves the equation:
(p(Q))N = C
as I've defined on page 2 of the attached document. This Q is the probability of running one experiment of population N and computing the range (e.g. 2Q) of the normally distributed random variable x...
Hello experts,
Thanks to discussions with Stephen Tashi for getting me this far.
See the problem statement in the attached PDF page 1. I need help solving for Qc in equation form, as a function of the other variables (N and C), preferably using erfc so I can program an accurate algorithm...
Wow, that's great Stephen. At first I was skeptical because of working with 1-(very small number), but in the end with the Taylor expansion of ex = 1+x, the 1 - ex simplifies to -x. Brilliant!
Thanks again Stephen,
If we use the Normal distribution with mean = 0 and sigma = 1, then the distribution N(x) simplifies to
N(x) = (1/(sqrt(2*pi))*e(-x*x/2)
If we can insert this into the appropriate "complementary" equation, then re-arrange terms and/or do a change of variables to...
Thanks Stephen,
(p(m))N=0.95
This equation is along the right track, thanks!. But, I find this places me working with numbers very close to 1. This is a problem because my values of N are very large, and there's only 16 digits in a computer's representation of a double-precision number...
Hi Stephen,
I think you're right. Let's set mu to 0 here (e.g. the mean of the distribution is 0).
For a random variable X with a given normal distribution N(mu=0,sigma), find an interval (-R,R) such that there is a 95% chance that when a given number n independent samples of X are taken...
Hi Stephen,
Thanks for your comments. Using your terminology, I want to compute the Nth order statistic multiplied by 2. That is, if we conduct N experiments of random variable x having normal distribution (mean=0), what's the largest value of x we'll observe (assuming some confidence level, or...
Hi Experts,
I'm working in industry and have an application requiring some expert knowledge on statistics/probability. I have a probability distribution function (PDF) for a Gaussian random variable. I know the standard deviation of the PDF. I also know total number of experiments conducted...