For questions about the expectation of a random variable: computations, upper/lower bounds, etc.
Questions tagged [expectation]
3734 questions
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Expectation of a Chi-squared distribution
I am to find out the value of this expectation : $$E \bigg(\frac{U^p}{U+V} \bigg),$$ where $U \sim \chi^2_1$ and $V \sim \chi^2_n$. $U$ and $V$ are independent.
Can anyone give me any hints about how to start this problem ?
Dwaipayan Gupta
- 285
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How to understand expectations
I am confused about the following expectations. Assume $z_n$ is an n-D random vector with multi-normal distribution and $a$ is an n-D real vector. Are these following two expectations identical?
$$First: E_{z_n}(a^T z_n)^3 $$
$$Second: E_{a^T…
victoriaabc
- 31
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How to find out the inequality related to expectation calculation
Let F be the distribution function of random variable X, that is $F(t)=Prob[X
P Pradhan
- 77
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Expectation calculation at infinity
While reading a paper, i came across the following Expectations:
Given that the $E\left\{e^2_{n-i-1}e^2_{n-j-1}\right\}=E\left\{e^2_{n-i-1}\right\}E\left\{e^2_{n-j-1}\right\}$ for $i\neq j$.\
Then as $n\rightarrow\infty$ …
fery
- 94
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Expected Driving Time
Suppose you need to drive from point $A$ to $B$, but must pass through point $C$ (one hour from point $A$) along the way. At point $C$ there are three roads you can take, $x$, $y$, and $z$ (and you take one at random each time). $x$ will take you to…
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Expectation of absolute difference of 2 repetition of a continuous random variable.
I was working on a problem below:
$X$ is a continuous random variable with cdf $F(x)$. If two values of $X$ are observed say, $X_1$ and $X_2$. Then show that $$E|X_1-X_2| = 4 \int^{+\infty}_{-\infty}x[F(x)-1/2]dF(x)$$
i.e. I want to show that…
skdhfgeq2134
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Expectation of Cauchy distribution
I have a problem, where I have to show that the Cauchy distribution has zero mean. I'm in doubt about if I have to show, that the expectation does not exists or it is zero?
The function is given by $f(x)=\frac{1}{\pi}\frac{1}{x^2+1}$ with the…
aa_x
- 315
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Expected number of ones
What is the expected number of bit $1$'s when writing a random integer from $1$ to $1024$ in binary?
I noticed that $1024 = 2^{10}$, so maybe linearity of expectation could help here?
William Yi
- 51
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2 answers
Expectation of norm of a random variable
Let $x_k$ be a random vector such that its expectation
$$
E[\Vert x_k \Vert]0$. Then can we say that
$$
E[\Vert x_k \Vert^2]
Ron
- 143
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Is the game fair?
In going over a question about expectation and payoff, I am a bit confused by one aspect of the solution.
Briefly, we have six sided fair die that is rolled three times. We are asked, considering the following rules, for what value of payoff $k$ is…
compguy24
- 421
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Expected Value of Truncated Random Variable
I have what appears to be a relatively simple question, but am struggling to understand how to go about answering it.
The general question is as follows:
What is the expected value of $S_{I}$, where:
$S_{I} = S$ if $S <3000 $
$S_{I} = 3000$ if $S…
Delvesy
- 749
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Easy mean-variance problem
Find the mean and variance of X, where X is the number of distinct results of a 12-sided die rolled 5 times (e.g. {3,11,12,3,11} returns X=3).
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Expectation of $1 - x^{0.5}$
Let $x$ be an indicator variable such that $E[X] = \frac{1}{3}$, calculate $E[1-x^{0.5}]$.
I'm having a hard time figuring out why this isn't equivalent to $E[1] - E[x^{0.5}]$ which would be $1-(\frac{1}{3})^{0.5}$
any help would be greatly…
user3358192
- 13
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What is the expected value of the score?
A card is drawn from a deck of 52. The score equal to its rank unless it is a court card (Jack, Queen or King) with a score of 10, otherwise equal to its rank and Ace counts as one.
What is the expected value of the score?
I am new to this and a…
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Find mean $\mu$ and variance $\sigma^2$ given $E[(X-1)^2] = 10$ and $E[(X-2)^2] = 6$
How do I find $\mu$ and $\sigma^2$ given $E[(X-1)^2] = 10$ and $E[(X-2)^2] = 6$?
I totally have no clue. Any idea/hint would be good. :)
Lawrence Wong
- 501