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
1
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1
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115
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How do we define the pdf in the multi-variate case and compute expectations?
Apologies if this is a very simple question but trying to work through a result in a paper made me realize I missed something a bit fundamental in my undergrad probability and analysis courses. Lets ...
- 115
1
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1
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645
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Expected Value of Exponential CDF
I am given the following CDF and I want to calculate its expected value:
$F(Y \leq y) =1-( 0.28e^{-0.5y} + 0.71e^{-0.25y})$
Creating the PDF:
$f(Y \leq y) = \frac{71\mathrm{e}^{-\frac{x}{4}}+56\mathrm{...
- 13
3
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1
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4k
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What is the expected value of half a standard normal distribution?
You have a normal distribution with mean of 0 and variance of 1. Keeping the same probabilities and focusing only on half of the distribution (other half has it's original probabilities but x values ...
- 3,263
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Mean and Variance of the Area of a Circle with Uniform Radius
A circle with a random radius R∼Unif(0,1) is generated. Let A be its area.(a) Find the mean and variance of A, without first finding the CDF or PDF of A.(b) Find the CDF and PDF of A.
So, quite ...
2
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3
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Expected value of a random variable in a range
I have a random variable $x$ with $E(x) = \mu$ and PDF $f(x)$ and CDF of $F(x)$.
Is there any way to represent the $E(x|x<\bar{x})$ in terms of $\mu$ and $f(x)$ or $F(x)$?
i.e. to write the ...
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