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How do you prove that if $ X_t \sim^{iid} (0,1) $, then $ E(X_t^{2}X_{t-j}^{2}) = E(X_t^{2})E(X_{t-j}^{2})$?
probability
expectation
independence
correlation
time-series
Expected Number of Flips for a Sequence of 4 to Repeat
probability
expectation
When $\Big[ uv \Big]_{x\,:=\,0}^{x\,:=\,1}$ and $\int_{x\,:=\,0}^{x\,:=\,1} v\,du$ are infinite but $\int_{x\,:=\,0}^{x\,:=\,1}u\,dv$ is finite
probability-distributions
definite-integrals
expectation
conditional-convergence
Why is $\mathbb{E}[X] = 1 + \sum^\infty_{k=1}\mathbb{P}(X > k)$ true?
probability
random-variables
expectation
Can you make money on coin tosses when the odds are against you?
probability-theory
expectation
martingales
gambling
Definition of Conditional expectation of Y given X.
probability-theory
expectation
A fair die is rolled 10 times. Define N to be the number of distinct outcomes. Find the mean and standard deviation of N.
probability
combinatorics
expectation
dice
Dumb question: Computing expectation without change of variable formula
probability-theory
measure-theory
reference-request
expectation
uniform-distribution
Prove that $E(|(X+Y)(X-Y)|) \leq 2\sqrt{1-\rho²}$, where $\rho$ is correlation.
probability
expectation
regression
Proof (confusion) of the product of two random variables of two sequences converge to XY
probability
probability-distributions
convergence-divergence
random-variables
expectation
Prove that $E\left(\frac{XY}{X^2+Y^2}\right) \geqslant 0$ for i.i.d. $X$ and $Y$
probability-theory
inequality
contest-math
expectation
Formula similar to $EX=\sum\limits_{i=1}^{\infty}P\left(X\geq i\right)$ to compute $E(X^n)$?
probability-theory
expectation
Average minimum distance between $n$ points generate i.i.d. with uniform dist.
probability-theory
expectation
supremum of expectation $\le$ expectation of supremum?
probability
proof-verification
convex-analysis
expectation
supremum-and-infimum
Expectation that the Distance Between two Points in the Unit Disc is 1
probability
expectation
Find $E[S]$ where $S$ is the standard deviation of a random sample from a $N(\mu,\sigma^2)$ population.
probability
normal-distribution
expectation
Proving $E[X^4]=3σ^4$
statistics
normal-distribution
expectation
Conditional expectation $E(X\mid XY)$ when $(X,Y)$ is standard normal
probability
normal-distribution
expectation
Variables defined as floor and fraction part from exponentially distributed random variable
probability
probability-distributions
expectation
Expectation of a Standard Normal Random Variable
integration
random-variables
normal-distribution
expectation
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