Linked Questions

Suppose $X_1, X_2 ...X_n$ are non-correlated and Gaussian random variables, all with mean value $\mu=0$ and variance=$\sigma$. Is there an expression for the distribution of $Z=\max(X_1, X_2, ... X_n)...

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 $F(x)^n$ and ...

If we have a sequence of random variables $X_1,X_2,\ldots,X_n$ converges in distribution to $X$, i.e. $X_n \rightarrow_d X$, then is $$ \lim_{n \to \infty} E(X_n) = E(X) $$ correct? I know that ...

Let $X_1, \dots, X_n \sim N(\mu,\sigma)$ be normal random variables. Find the expected value of random variables $\max_i(X_i)$ and $\min_i(X_i)$. The sad truth is I don't have any good idea how to ...

Which of the following is more surprising? In a group of 100 people, the tallest person is one inch taller than the second tallest person. In a group of one billion people, the tallest person is one ...

In the coupon collector's problem, let $T_n$ denote the time of completion for a collection of $n$ coupons. At time $T_n$, each coupon $k$ has been collected $C_k^{n}\geqslant 1$ times. Consider how ...

Let $X_1,\ldots,X_n$ be i.i.d $\mathcal{N}(0,1)$ random variables. I am trying to prove that \begin{align} (a)\ \ \mathbb{E} \left[ \max_{i}X_i\right] & \asymp\mathbb{E} \left[ \max_{i}|X_i|\...

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 ...

Let $B_i(n,1/2)$ be independent identically distributed binomial random variables. How can one derive lower and upper bounds for the expected value of the maximum of $n$ such random variables? I am ...

I am looking for a reference to cite, for the following "folklore" asymptotic behaviour of the maximum of $n$ independent Gaussian real-valued random variables $X_1,\dots, X_n\sim \mathcal{N}(0,\sigma)...

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 ...

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 $x_1$ ...

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 ...

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) ...