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seen Sep 11 at 14:13

Aug
31
comment Prove a random variable has normal distribution
Thanks! I think the first part is clear now. For the second question, if the support of the measure of $(X,Y)$ is not all open sets of $\mathbb{R}^2$ then it doesn't have normal distribution? But unfortunately I'm still at a lost as to how to draw that.
Aug
31
comment Prove a random variable has normal distribution
As to the second part,does not $E(XY)=0$ fix an $a>0$ which might not be the constant given at the start? Which in turn would mean we can't arrive at a contradiction. Or have I completely misunderstood something here?
Aug
31
comment Prove a random variable has normal distribution
In the first part is $Z$ the $Y$ from the question and $Y$ is $X$ from the question? Could you explain the equality $Pr(-Y \in A, |Y|>a) = Pr(-(-Y)\in A, |-Y| >a)$, specifically the $-(-Y)\in A$ part? I'm afraid I don't quite understand it.
Aug
30
asked Prove a random variable has normal distribution
Aug
13
comment If $\sum_{n \geq 1}X_n$ converges a.s. then $\forall a > 0: \sum P(|X_n|>a) < \infty$
I see! Thank you!
Aug
13
comment If $\sum_{n \geq 1}X_n$ converges a.s. then $\forall a > 0: \sum P(|X_n|>a) < \infty$
But how do I know that $X_n \rightarrow 0$ a.s.? Can one show this from the fact that the sum converges a.s.?
Aug
13
asked If $\sum_{n \geq 1}X_n$ converges a.s. then $\forall a > 0: \sum P(|X_n|>a) < \infty$
Aug
5
asked Complexity of the power method
Jul
23
comment Find angle of incomplete rotation matrix
Thanks! I hadn't seen your first fact before!
Jul
23
asked Find angle of incomplete rotation matrix
Jul
2
awarded  Curious
May
7
comment Prove $||A||_2 = max_{x \neq 0, y \neq 0}\{\frac{|\langle y,Ax \rangle|}{||x||\cdot ||y||}\}$ for $A\in \mathbb{K}^{n\times m}$
Thanks! That cleared everything up!
May
7
comment Prove $||A||_2 = max_{x \neq 0, y \neq 0}\{\frac{|\langle y,Ax \rangle|}{||x||\cdot ||y||}\}$ for $A\in \mathbb{K}^{n\times m}$
I'm afraid I don't quite know what to do with that information. SVD leads me to: $||A|| = max_{||v||=1} \langle v, V \Sigma^2 V\text{*}v\rangle$ which I don't know what to do with
May
7
asked Prove $||A||_2 = max_{x \neq 0, y \neq 0}\{\frac{|\langle y,Ax \rangle|}{||x||\cdot ||y||}\}$ for $A\in \mathbb{K}^{n\times m}$
May
5
awarded  Tumbleweed
Apr
28
asked Find $\underset{\omega}{\min}$ $\underset{\beta \in \sigma(A)}{\max}$ $|\frac{\omega - \beta}{\omega + \beta}|$
Apr
2
asked Example: Sum of non-commuting matrices is not normal
Jan
31
comment Show $\sqrt{1 + (\int_{\Omega} h d\mu)^2} \leq \int_{\Omega} \sqrt{1+h^2} d\mu$
aaah right! thanks so much!
Jan
31
accepted Show $\sqrt{1 + (\int_{\Omega} h d\mu)^2} \leq \int_{\Omega} \sqrt{1+h^2} d\mu$
Jan
31
asked Show $\sqrt{1 + (\int_{\Omega} h d\mu)^2} \leq \int_{\Omega} \sqrt{1+h^2} d\mu$