For questions about the expectation of a random variable: computations, upper/lower bounds, etc.
Questions tagged [expectation]
3734 questions
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Proof: Cauchy distribution no moments
How can I prove the Cauchy distribution has no moments?;
$$E(X^k)=\int_{-\infty}^\infty\frac{x^k}{\pi(1+x^2)}\,\mathrm dx.$$
I can show for $k=1$ and $k=2$ that the moment would be infinity, and therefore doesn't exist.
However, how can I show it…
Sha Vuklia
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4 fair dice are rolled. Find the expected total of the rolls.
I'm using expectation in this problem
If the expected value of 1 roll is:
E(X) = (1 * 1/6) + (2 * 1/6) + (3 * 1/6) + (4 * 1/6) + (5 * 1/6) + (6 * 1/6)
= 1/6(1+2+3+4+5+6)
= 21/6
= 7/2
Then would the expected total of 4 rolls be:
7/2 * 4 = 14?
dj5
- 29
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Expectations of outcomes
$X_1, X_2, \ldots,X_{50}$ represents the 50 outcomes of 50 independent fair coin flips. $$P(X_i=0)=P(X_i=1)=0.5$$ I am trying to analyze the different possibilities of $\operatorname{E}(X)$ and $\operatorname{var}(X)$. Define $X$ to be $X = X_1 -…
Jonathan
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P(x>0) is positive for bet but expected value negative?
Summary:
I have a bet where, for one bet, the probability of getting a positive amount of money is positive. However, the expected value is negative. Should I take this bet?
What is useful to think about when making this choice?
Longer version:…
zthomas.nc
- 427
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expectation value of number of drawn white balls
We have $5$ white balls, $3$ black and $2$ red in urn. We draw one after another ball with returning till we thrown red ball. Let $X$ be a number of drawn white balls. Calculate $\mathbb{E}X$.
I've started from defining $X_i$ such that $X_i=1$ when…
wiwnes691
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Does $\log(E[U]) = E[\log(U)]$?
In particular, I have
$$u = e^{-\gamma c_{t}}$$
Is it true that ($c_{t} > 0 \ \gamma \in \mathbb{R})$,
$$\log(\mathbb{E}\left[e^{-\gamma c_{t}} \right]) = \mathbb{E}\left[\log(e^{-\gamma c_{t}}) \right]$$
where $\mathbb{E}$ denotes expectation. …
user43395
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rewriting an expectation of a minimum of a maximum into an integral
I am looking for a way to rewrite the following equation into an integral for a general distribution of the r.v. $X$:
E[$\min\{\max(0;q_1 - X) + q_2; \alpha X \}$]
where $q_1, q_2$ and $\alpha$ are constants. Eventually I want to take the…
AnkeK
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Why moments of expectation are known as "moments"
I am studying moments of expectation, and seen the formulas for computing the moments. There is one thing I am not clear of, and not getting answer for that.
Why moments are named as moments? To my understanding, the word "moment" has relationship…
Osman Khalid
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Clarifications for linearity of expectation
For linearity of expectation to work, do the random variables have to be from the same experiment?
S there are two random variables X and Y on the same sample space, which assigns real values $X(s)$ and $Y(s)$ to to very outcome $s$ of an…
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Expected value of a circuit given $f_{X, Y}(x, y) = k(x + y)$
HW problem, not sure where I'm going wrong on this.
Find $E(R)$ for a two-resistor circuit similar to the one described in Example 3.9.2, where $f_{X, Y}(x,y) = k(x + y)$, | $10 ≤ x ≤ 20$, $10 ≤ y ≤ 20$
Example 3.9.2 shows resistors set up in…
David
- 259
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For what g, $E(X|g(X)=0$ where $X$ is standard normal?
I know if $g(X)=X^2$, the equality holds. Is there any other $g$? How can we generalize the case $g(X)=X^2$ (other than $g(X)=X^{2k}$?
bankrip
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