All Questions
6 questions
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Question on the proof step in the theorem 1 of the Gap statistic paper
From the Gap statistic paper, during the proof for the theorem 1, we can see the below equality (p. 422),
$\begin{aligned} \operatorname{var}(X) & =\frac{1}{2} \int_{-\infty}^{\infty} \int_{-\...
- 303
3
votes
1
answer
177
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Calculate expected values E(x) & E(y) & variance of x & y of joint PDF, which was previously transformed from Polar to Cartesian
Given two independently uniform distributed random variables angle $\theta \in [0,2\pi]$ and radius $r \in [0,1]$.
I obtain for the joint density function with polar coordinates: $$ f_{r,\theta}(r,\...
- 33
0
votes
1
answer
71
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Expectation of ratios of probability density functions
I'm trying to solve/simply the expression below:-
$\large \mathbb{E_{x \sim b(x)}} B\ [log\left(1 - \frac{A\ a(x)}{2\ c(x)}\right)]$,
or
$B \large \int_{x}b(x)log\left(1 - \frac{A\ a(x)}{2\ c(x)}\...
- 33
2
votes
1
answer
290
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Expectation of $h \circ X$
I'm only starting to learn statistics.
The definition I've been given for the expected value (expectation) of a continuous random variable X with probability density function (PDF) $f_X$ is the ...
2
votes
1
answer
1k
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Expectation using CDF
I have a problem understanding the solution of an exercise:
$F_x(x) = 1-(\frac{\sqrt{3}}{2}x + \frac{3}{2})^{-3}$ for $x \geq \frac{-1}{3} \sqrt{3}$, $0$ elsewhere
and i am asked to compute the ...
- 73
3
votes
2
answers
256
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What is the expected partial value function really called?
If f is a pdf, the integral of xf(x) over the entire range where f(x) > 0 gives, of course, the expected value. Suppose that integrate the same function, xf(x) from negative infinity up to t, ...
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