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user321627
  • Member for 6 years, 6 months
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30 votes
5 answers
3k views

What is the purpose of defining a Hilbert Space?

6 votes
1 answer
131 views

For two random variables $X_1, X_2$, is it always necessarily the case that $E(e^{X_2}\mid e^{X_1}) = E(e^{X_2}\mid X_1)$?

5 votes
0 answers
203 views

Finding the mean of $X_t = \int_0^t sW_sdW_s$

5 votes
0 answers
2k views

Finding a bound on the maximum of the absolute value of normal random variables

4 votes
1 answer
84 views

Coefficient matching proof that $e^{\alpha x-\frac{1}{2} \alpha^2}=\sum_{n=0}^{\infty} \frac{1}{n!}H_n(x)\alpha^n$, where $H_n(x)$ are Hermite poly.?

4 votes
3 answers
7k views

In a ring that is the direct product of two fields, why isn't it a field? [duplicate]

4 votes
1 answer
128 views

If $X_1, \ldots, X_n \sim t_\nu$, a t-distribution with $\nu >1$, how to show $E\left(\max_{1 \leq i \leq n}|X_i|\right) = O\left(n^{1/\nu}\right)$?

4 votes
0 answers
57 views

How is the limit infimum of sets different from the limit infimum of a sequence of real numbers? [duplicate]

4 votes
2 answers
926 views

Suppose $X_1, \ldots, X_n$ are iid standard Cauchy random variables, does $\frac{1}{n}\sum_{i=1}^{n}X_i$ converge in probability or almost surely?

4 votes
1 answer
1k views

If $\Sigma$ is a covariance matrix, how to obtain the decomposition $\Sigma = \Sigma^{1/2}(\Sigma^{1/2})^T$ from Cholesky Decompositon?

4 votes
1 answer
3k views

What does it mean for a probability model to be "well-specified" or "misspecified"?

4 votes
3 answers
201 views

If $X \sim N(\mu, \sigma^2)$, and $Y$ is another random variable, is it an abuse of notation to write $p(X|Y, \mu, \sigma^2)$?

4 votes
2 answers
530 views

What is a simple to understand example (i.e. adjacency matrix) of a vertex transitive graph?

3 votes
2 answers
52 views

How to compute the limit of $\lim_{n\to \infty}\left(1-e^{-nk}\right)^n$ for $k>0$ a constant?

3 votes
2 answers
107 views

Finding the expected value of of $\int_0^s \sqrt{t+B_t^2}dB_t$?

3 votes
5 answers
193 views

How to evaluate the integral $\int_0^{\infty} e^{-\frac{1}{2}\left(x^2+ \frac{c}{x^2}\right)}dx$? [duplicate]

3 votes
1 answer
751 views

Is it possible to show associativity of multiplication in a field?

3 votes
1 answer
428 views

What is the variance of the expected time until one can construct an ABRACADABRA sequence?

3 votes
1 answer
627 views

Proving that if $V$ is an inner product space and $U_1, U_2$ are subsets, then $U_1 \subset U_2$ if and only if $U^{\perp}_2 \subset U^{\perp}_1$

3 votes
0 answers
56 views

What is wrong with using Kolmogorov's inequality for finding the expectation of the maximum of normal random variables? [duplicate]

2 votes
0 answers
45 views

Are there any problems in probability theory where it cannot be solved or defined with respect to Borel sets but only with Lebesgue measurable sets?

2 votes
1 answer
93 views

If $X_1, \ldots, X_n \sim N(0,1)$, then $E(\max_{1 \leq i \leq n}X_i) = O(\sqrt{\log\ n})$. What does this mean for prediction of extreme events?

2 votes
2 answers
242 views

How to intuitively understand why for a sequence of a sets $A_n$, $\liminf_{n}A_n \subseteq\limsup_{n}A_n$?

2 votes
1 answer
693 views

Why does this least-squares approach to proving the Sherman–Morrison Formula work?

2 votes
2 answers
69 views

How to show that the minimal field between $\mathbb{Z}$ and $\mathbb{R}$ is $\mathbb{Q}$?

2 votes
2 answers
1k views

Negating an existential quantifier over a logical conjunction?

2 votes
0 answers
302 views

How to find the variance of $\int_0^t B_s^2 ds$ where $B_s$ is a standard Brownian motion random variable?

2 votes
3 answers
71 views

How to figure out which of three equations: $y=-2x+1, y=2x+1, y=x+1$ is linearly dependent on the others?

2 votes
1 answer
63 views

How to solve the multiple integral $\int\sin^{p-2}(\theta_1)\sin^{p-3}(\theta_2) \cdots \sin(\theta_{p-2})\ d\theta_1d\theta_2\cdots d\theta_{p-1}$?

2 votes
1 answer
3k views

What is the geometric interpretation of least squares fitting when the system is under-determined?

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