All Questions
Tagged with expected-value probability
584
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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 ...
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Expected value of a decreasing function of two random variables
My question is exactly equal to the question posted at Expected value of decreasing function of random variable versus expected value of random variable with just one extra assumption: the two random ...
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Probability algorithm on strings
Let $x$ be any binary string $\in (0,1)^*.$
The majority language is given by:
$$\text{MAJ}:=\{x\in (0,1)^*:\sum_{i=1}^ {|x|}x_i>\frac{|x|}{2}\},\text{where $x_i$ is the $i$-th position value(...
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Tight upper bound on the function of expected value
Let $R$ be a positive integer, $\mathcal{X}$ be the sample space and $x \in \mathcal{X}$ be an event of the sample space; $P(x)$ denotes the probability of occurrence of event $x$. The problem is to ...
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What conditions are there on the exponent $p$ such that $\underset{\mu}{\arg\min}\left\{\mathbb E\left\vert X-\mu\right\vert^p\right\} $ must exist?
Let $X\sim F(x)$ be a (univariate) random variable defined by distribution function $F$. If the expected value exists, it is equal to $
\mathbb E[X] = \underset{\mu}{\arg\min}\left\{\mathbb E\left\...
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2
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Expected value of decreasing function of random variable versus expected value of random variable
Given two random variables $X_1$ and $X_2$ (same sample space $\mathcal{X}$) that
$$\mathbb{E}[X_1]=\int_{\mathcal{X}}xf_1(x)dx > \mathbb{E}[X_2]=\int_{\mathcal{X}}x f_2(x)dx$$
Can we say that $\...
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properties of a expectation for a non-negative random variable
Say I have a non-negative discrete random variable $X$ (values of $X$ can be mapped to integers $(0, 2^n -1)$ for $n \in \mathbb{Z}$) and an associated distribution $P(X)$. Given a non-negative scalar ...
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How to find probability from $E[X^n]$?
It is given that $E[X^n] = \frac{2}{5}(-1)^n + \frac{2^{n+1}}{5}+\frac{1}{5}$, where $n=1,2,3,\ldots.$
I need to find $P(|X-\frac{1}{2}| > 1)$.
What my approach is :
I have opened the modulus ...
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$E(XY)$ for a truncated bivariate normal
If $(X, Y)$ follows a bivariate Gaussian distribution with mean ${\bf \mu}$ and covariance ${\bf \Sigma}$ with truncation bounds $(a_x, b_x, a_y, b_y)$, can we compute $E(XY)$ in closed form? If not, ...
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Scaling the conditioned random variable does not change conditional distribution, why?
Given two random variables $X$ and $Y$, I know intuitively that
$$
\mathbb{E}[X\,|\,Y]=\mathbb{E}[X\,|\,cY],
$$
where $c$ is some non-random constant. My intuition tells me that scaling the ...
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Describing guaranteed profit situations which are stronger than just 'superfair wager'
Context.
I am tutoring a final year secondary school student in mathematics. To illustrate the principles of card-counting in a situation of sampling without replacement, I've decided to show her a ...
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Guessing the size of a set based on number of repeated random draws
I am trying to study a problem in algebraic number theory through a set of computational experiments. I have an enormous (say, of size $X$) family $\mathcal{F}$ of polynomials and I'm trying to ...
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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 ...
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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 ...
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Question regarding probability and maximum possible variance
I have the following question:
Suppose we have a set of 10 numbers (1, 2, ... , 10), each with a certain probability tagged to it.
Is it true that the highest possible variance is achieved when 1 and ...
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