All Questions
Tagged with expected-value distributions
214
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Computing a Confidence Interval for E[X] when PMF is given
I am given a Probability Mass Function for a discrete random variable.
From the PMF I computed the Expected Value $E[X]$, the Variance $V[X]$ and the Standard Deviation $S[X]$.
Here is an example (the ...
- 566
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1
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275
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Probability algorithm on strings
Let $x$ be any binary string $\in (0,1)^*.$
The majority language is given by:
$$\text{MAJ}:=\{x\in (0,1)^*:\sum_{i=1}^ {|x|}x_i>\frac{|x|}{2}\},\text{where $x_i$ is the $i$-th position value(...
- 69
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Why does $E(V_n/(n+2)-1)^2=2/(n+2)$ when $V_n\sim\chi^2(n)$?
I was reading some lecture notes when I saw a simplification I didn't understand. Specifically, we have $V_n\sim\chi^2(n)$. It was then written then
$$E\left(\frac{1}{n+2}V_n-1\right)^2=\frac{2}{n+2}.$...
- 155
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51
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Find $E[Y]$ when $f(x,y) = \frac{x}{3}e^{-xy}$
Truth be told, I don't really have an issue with this problem in general, but in it's calculation. Let me explain.
We need to find $E[Y]$ when $f(x,y) = \frac{x}{3}e^{-xy}$, $1<x<4$ and $y>0$...
- 195
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18
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Expected average distance in greedy matching on a circle
Now we have several independent and identically distributed random variables following the uniform distribution on the interval [0, 1].They are denoted as $x_1, x_2, x_3, ..., x_m$ and $y_1, y_2, ..., ...
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37
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Ratio of Normal Distributions [duplicate]
Suppose I have two independent random variables, $X \sim N(\mu_1,\sigma_1^2)$ and $Y \sim N(\mu_2,\sigma_2^2)$ with $\mu_1,\mu_2 > 0$.
How can I compute/estimate
$$ \mathbb{E}\left[\left\lvert \...
- 119
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2
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107
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The training error of best hypothesis
Let $\mathcal{X}$ and $\mathcal{Y}$ denote the domain set and label set respectively. Also let $\mathcal{D}$ be a distribution over $\mathcal{X}$ and $f:\mathcal{X} \to \mathcal{Y}$ be the true ...
- 67
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62
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Confused on Kullback-Leibler divergence being invoked without proper definition
I am trying to understand how authors of the DDPM paper in appendix A, made the leap from equation 21 to equation 22.
Specifically, it is not clear to me how they managed to convert the first term of ...
- 1,805
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85
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How to find $\mathbb{E} \left[\frac{\bar{\mu}}{\bar{\sigma}^2}\right]$?
I asked the same question on math stacks: MathStacks:, and some user suggest to ask it here for better insight. So this question has found interest in many research problems, but there have been no ...
- 11
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Expectation of product of sample averages
I have a bunch of iid random variables $X_i\sim q$ and I have defined other random variables $A_i = a(X_i)$ and $B_i = b(X_i)$. Then I bumped into the following expression
$$
\begin{align}
\mathbb{E}\...
- 2,236
5
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1
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198
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expectation value, distribution function and the central limit theorem
The problem goes thus:
${\{X_n\}}$ is an $iid$ sequence of random variables with mean 0 and variance $\sigma^2$. If the third moment is finite, show that $$\lim_{n \to \infty} \mathbb{E} \left(\left(...
- 153
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113
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"Almost surely" used in an expectation
Let $(\mathsf{X}, \mathcal{X})$ be a measurable space, $\pi(dx)$ be a probability measure on it, and $K:X\times\mathcal{X}\to[0, 1]$ be a Markov kernel. I have the following property
$$
\int K(x, A) \...
- 657
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39
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Given two rvs $X$ and $Y$, if $X Y = Z$, is it possible to change the mean and sd of $X$ without changing the mean and sd of $Y$ and $Z$
I have two lognormal rvs $X$ and $Y$, and a third rv $Z$ which is the product of the former two. I know the mean and standard deviation of the three.
Is it possible to calculate an alternative pair of ...
- 113
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Convergence of $E(|X|^r)^{\frac{1}{r}}$ [closed]
For a random variable $X$ on $[0, 1]$ with $F(1) = 1$ and $F(x) < 1$ for all $x < 1$, show that $E(|X|^r)^{\frac{1}{r}} \to 1$ as $r → ∞$. If $F$ is such that $F(x) < 1$ for all $x ∈ \mathbb{...
- 311
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1
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57
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Distribution Estimator dependent on sample size
I have a known distribution for my population, and it is very right skewed. Let's say Lognormal with mu = 0 and sigma = 3. The mean of this distribution is about 90, and the median is 1.
For a given ...
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