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### Generating a nonrandom sequence which has a normal distributed density

I need to create an algorithm in a computer program (Fortran90) which generates a sequence of $n$ (between $10$ and $10^6$) numbers $z$ that follow a normal distribution. Restrictions: Has to ...
Let $X_1,\dots,X_n$ be i.i.d. random variables, each uniformly distributed on $[0,1]$. Let $\hat F_n$ be their modified empirical distribution function, i.e., $$\hat ... 0answers 72 views ### Expectation involving a maximum of a sequence of i.i.d. Gaussians Let X_1,\ldots,X_n be a sequence of i.i.d. standard Gaussian random variables. Denote the maximum of this sequence by M_n. I am interested in evaluating the following expectation: ... 0answers 58 views ### Asymptotic (in)dependence of a maximum of an i.i.d. sequence of Gaussian random variables on a single random variable in this sequence Suppose that I have a sequence of n i.i.d. standard Gaussian random variables X_1,\ldots,X_n where X_i\sim\mathcal{N}(0,1). Denote the maximum of this sequence by M_n=\max(X_1,\ldots,X_n). I ... 2answers 273 views ### Convergence of a sequence involving the maximum of i.i.d. Gaussian random variables It's well known that, for a sequence of n i.i.d. standard Gaussian random variables X_1,\ldots,X_n, where X_\max=\max(X_1,\ldots,X_n), the following convergence result holds: ... 0answers 112 views ### Maximum of a sequence of almost-identical independent normal random variables Take a sequence X_1,\ldots,X_n where each X_i\sim\mathcal{N}(\mu,\sigma^2) is an i.i.d. normal random variable. Denote by X_\max the maximum of this sequence. A well-known fact about ... 0answers 28 views ### What is the product of the average x and the average (1/x), where x is normally distributed. Has anyone ever seen a solution for the following...?$$ \left( \frac{1}{n}\sum_{i=1}^{n} x_{i} \right) \times \left( \frac{1}{n} \sum_{i=1}^{n} \frac{1}{x_{i}}\right)  where the x values are from ...
The Pascal triangle can be described by the recurrence: $P(n,1)=1, k>1: P(n,k) = P(n-i,k-1) + P(n-i,k)$ This well known triangle has the basic properties that the ratios of consecutive ...