# Tagged Questions

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### limit of limit superior w.r.t truncated set

Let $\Theta\subseteq\mathbb{R}^d$ is open set and $(\cal X, \cal A)$ be a measurable space . For every $\theta\in\Theta$, suppose that $P_\theta$ is a probability measure on $(\cal X, \cal A)$. ...
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### What is the value of the following integral? ( including the inverse of the CDF of the standard normal distribution)

What is the value of the following integral? $$f(\alpha)=\int_0^\alpha [b-c \Phi^{-1}(1-\beta)] d\beta$$ where $0<= \alpha=<1$ ,b and c are constants, and $\Phi$ is the cumulative ...
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### Joint To Marginal Density : Can't figure it out.

Here goes the problem: Problem: Suppose $X$ and $Y$ have the joint density function: $f(X,Y) = c \sqrt{1 - x^2 - y^2}, \,\,\,\,\, x^2 + y^2 \leq 1$ Find $c$. ...
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### How do i integrate this $f(x)$ to show that it's probability density fn? [closed]

I am trying to show that $$f(x) = \exp(-x-e^{-x})$$ is p.d.f. But when I integrate it, I dont get $1$? How would you integrate it?
When we draw $n$ samples of Laplace-distributed random variable such that $n=2k+1$ and the location parameter is zero, the median $x$ (or the $k$-th order statistic) has the following p.d.f.: ...
This is the last part of a three part problem on characteristic functions, and it's been driving me crazy over the last few days. Any help would be most appreciated. $X_1,X_2, \ldots, X_n$ are ...