# Linked Questions

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### expectation of maximum of iid random variables from normal distribution. [duplicate]

1) How to find expectation of max of random variables , i.e : $\mathbb{E}[max(x_1,x_2,\dots,x_n)]$ where $x$ are IID random variables from $\mathcal{N}(\mu,\sigma^2)$. I know that CDF is $F(x)^n$ ...
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### What is the maximum expected value in a selection?

Here's a hypothetical problem: assume that mean diameter of a tennis ball is 6.7 cm. Assume that the diameter is normally distributed with a standard deviation of 0.1 cm (I may have picked up a weird ...
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### Variance of a max function

Say $x_1$ and $x_2$ are normal random variables with known means and standard deviations and $C$ is a constant. If $y = \max(x_1,x_2,C)$, what is $\mathrm{Var}(y)$? Well, I forgot to tell that $x_1$ ...
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### Expected maximum absolute value of $n$ iid standard Gaussians?

I have a problem where my errors are normally distributed and I want to know what the expected maximum error is if I repeat the process $n$ times. What is the smallest constant $C$ such that the ...
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### Distribution of largest sample from normal distribution.

Given $n$ independent random variables $X_i$ with normal distribution, mean $\mu$, variance $\sigma^2$, what is the distribution of $\max\limits_{i=1}^n(X_i)$ ? In particular I am interested in ...
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### Range of i.i.d. normal random variables

Let $X_1, \dotsc, X_n$ be i.i.d. standard normal random variables. Define the range $R \in \mathbb{R}_{\geq 0}$ as $R = \max \{X_1, \dotsc, X_n\} - \min \{X_1, \dotsc, X_n \}$. I am looking for a ...
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### PDF for minimum and maximum of n independent Gaussian random variables

Stimulated by the problem Let $Z\sim N(0,1)$ be a random variable, then $E[\max\{Z,0\}]$ is? I came up with this problem: Let $x_i, i=1..n$ be $n$ independent random variables $\sim N(0,1)$. 1) ...
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### Impact of random numbers on the eigen-values

How do the eigen-values of the following tridiagonal matrix ($A$) change when adding random numbers $R_i$ (with a normal distribution with the mean 0 and variance $m$) to its diagonal. A is a square ...
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### 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: \tag{1}\...

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