Tagged Questions
2
votes
1answer
45 views
Probability proofs using ordered samples
Given an ordered i.i.d sample $X_{(1)}, \dots, X_{(n)}$ from a continuous distribution $F(x)$. How can it be shown that:
(1) $\text{Pr}(X_{(k)} \leq x) = \text{P}r(N(x) \geq k)$
where $N(x)$ is the ...
1
vote
1answer
329 views
How to show order statistic is sufficient
I have some trouble showing sufficiency for largest order statistic ${x}_{n}$.
This is from Casella's text, problem 1.6.3.
Let ${p}_{\theta}$ be a density function.
${p}_{\theta}{x}=c({\theta})f(x)$ ...
3
votes
2answers
727 views
Problems with extremum of two uniform random variables
Here is the problem from the book:
Let $X = \min(U,V)$ and $Y = \max(U,V)$ for independent $\text{uniform}(0,1)$ variables $U$ and $V$. Find the distributions of a) $X$; b) $1-Y$; c) $Y-X$.
I ...
