query: Expectetion of $Y^{\alpha}$ with $\alpha >0$
positive_passages.docid: 14764
positive_passages.text: Explain why $E(X) = \int_0^\infty (1-F_X (t)) \, dt$ for every nonnegative random variable $X$
negative_passages.docid: 123039
negative_passages.text: If $0<\alpha < 1$ and $d(x,y)$ is metric, show that $((d(x,y))^{\alpha}$ is metric.
negative_passages.docid: 57639
negative_passages.text: Show there exists an $\alpha\in F_{p^n}$ such that $\alpha +\alpha^p+\alpha^{p^2}+\cdots+\alpha^{p^{n-1}}\neq 0$
negative_passages.docid: 5350
negative_passages.text: Explain why $E(|X|^p)=p\int_{0}^{\infty}y^{p-1}P(|X|>y) dy$
negative_passages.docid: 38636
negative_passages.text: A basic question about exponentiation: when is $a^{xy}=(a^x)^y$?
negative_passages.docid: 83873
negative_passages.text: Find $E(|X-Y|^a)$ where $X$ and $Y$ are independent uniform on $(0,1)$
negative_passages.docid: 132920
negative_passages.text: Help with proof that the expected value of $x_i$ is $\bar{X}$
negative_passages.docid: 93460
negative_passages.text: WLLN: can expectation exist but be infinite?
negative_passages.docid: 27347
negative_passages.text: Verify that $\left|\int_{\gamma} \exp(iz^2)dz\right| \leq \frac{\pi\big(1-\exp(-r^2)\big)}{4r}$ where $\gamma(t)=re^{it}$, for $0\leq t \leq \pi/4$.
negative_passages.docid: 89883
negative_passages.text: Find the leading order uniform approximation when the conditions are not $0<x<1$
negative_passages.docid: 97720
negative_passages.text: Asymptotic behavior of $\sum\limits_{k=1}^n \frac{1}{k^{\alpha}}$ for $\alpha > \frac{1}{2}$
negative_passages.docid: 132595
negative_passages.text: $\sup_{0 \leq M \leq I_{\mathcal{H}_1}} \frac{\operatorname{Tr}[\rho M]}{\operatorname{Tr}[\sigma M]}$ satisfies Data Processing Inequality
negative_passages.docid: 106316
negative_passages.text: Finding a bound on the maximum of the absolute value of normal random variables
negative_passages.docid: 135941
negative_passages.text: Derivative of $|x|^\alpha$
negative_passages.docid: 79307
negative_passages.text: How to analyze $\sup_{x>0}|e^xf(x)| < \infty$ and $\sup_{n\in\mathbb{N}} |f^{(n)}(0)|< \infty$?
negative_passages.docid: 157917
negative_passages.text: Calculate the leading order asymptotic behaviour (with two maxima)
negative_passages.docid: 89544
negative_passages.text: Expectation of a random variable that takes points in the natural numbers