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Proving the convergence of the maximum of Uniform Distribution
I have a random sample of size $X_1, X_2, .., X_n$ following $U(0,2)$. I need to prove that $X_{(n)}$ which is the maximum ordered statistics will converge to $2$ in probability and almost surely.
I ...
- 1,048
2
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2
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Distribution of extreme values, case of uniform
Question: For $U_1 , \dots, U_n$ i.i.d. $U \sim \mathrm{unif}[0,1]$, we want to find the asymptotic distribution of $Z_n = n(1-U_{(n)})$ where $U_{(n)} = \max(U_1 , ... , U_n)$
I found this: ...
- 770
2
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2
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Determine density of $\min(X,Y)$ and $\max(X,Y)$ for independently uniform distributed variables
Two independent random variables, $X$ and $Y$, are uniformly distributed on the unit interval $(-1,1)$.
Determine the density for $U=\min(X,Y)$ and for $W=\max(X,Y)$
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