# order statistics

1. ### Number of ways to divide 12 people into 3 teams, where order matters or it does not

How many ways are there to categorize 12 people into 3 teams of 4? if order does not matter: 12!/4!4!4!3! or ((12 choose 4)(8 choose 4) (4 choose 4))/3! if order matters across teams: 12!/4!4!4! (or (12 choose 4) (8 choose 4) (4 choose 4)) Then, if order matters within teams or if order...
2. ### Expected Value of Y = max (X1, X2, X3, .... , Xn)

I'm having a hard time figuring out what the expected value of Y = max(X1, X2, X3, ... , Xn) with pdf (x;θ) = 2x/θ^2. So it is the nth value of order statistics Y1<Y2<Y3.....<Yn. Does anyone know?
3. ### Conditional expectation of maximum given minimum of order statistics

Let we have $X_1 ... X_n$ - iid random variables with $F(x)$ - distribution function. So we have $X1:n$ and $Xn:n$ - minimum and maximum. Help me please with counting conditional expectation $E(Xn:n|X1:n=x$) in terms of $F(x)$ ?
4. ### Order Statistics Problem

Hi there I have random variables X1,X2,X3,...,XN which are I.I.D. Each of these random variables are Erlang Distributed. X=min{X1,...,XN}. Now the sample size N changes with each iteration according to the following rule If Yn<=X<Yn+1 Then N=2^n where n is an element of...
5. ### Order statistics, sample median

Hi! Can you help me with this: we have X=(X1, X2, ... Xn) - iid, Xi ~ N(m,1), I need to prove that distribution of med(X)-X(j) is the same as distribution of X(n-j+1)-med(X), where med(X) is a sample median and X(j) is j-th order statistic.
6. ### Help with unbiased estimators and efficiency

Suppose that Y1, Y2, ..., Yn constitute a random sample from the density function f(y|t) = e^-(y-t), y>t where t is an unknown positive constant a. Find an estimator t1(hat) for t by the method of moments b. Find an estimator t2(hat) for t by the method of maximum likelihood c...
7. ### Expected Value of Order Statistics from Standard Normal Distribution

Question: Find the expected value of the largest order statistic in a random sample of size 4 from the standard normal distribution. Remarks: I got the only answer to this question without any derivation or proof. The definite integral is very difficult, please help with the integral. Please...