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user321627
  • Member for 6 years, 7 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

5 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
533 views

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

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
931 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?

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
194 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
756 views

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

3 votes
1 answer
429 views

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

3 votes
1 answer
632 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]

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?

2 votes
1 answer
90 views

For $Y \sim Beta(n, 1)$, showing that $\frac{1}{n}log\int_{Y}^1 x^{-n}e^{-(x-1)^{-2}}dx$ converges in probability to $-\infty$?

2 votes
1 answer
58 views

If $\sqrt{n}(\widehat{\theta}_{n}-\theta) \to N(0, \frac{1}{I_1(\theta)})$, what does $\sqrt{n}(\widehat{\theta}_{kn}-\theta)$ converge to?

2 votes
1 answer
1k views

For the Central Limit Theorem, why does the $\sqrt{n}$ term represent the convergence rate?

2 votes
1 answer
187 views

What is the intuition behind the definition of a Markov Chain being $\pi$-invariant?

2 votes
0 answers
99 views

If $f(y\mid\theta)\sim N(\theta, 1)$, how to find the asymptotic distribution $f\left(y\mid\hat{\theta}_n^{MLE}\right)$?

2 votes
0 answers
97 views

In machine learning and statistics, why does the lasso path slope down to the right?

2 votes
3 answers
1k views

Why is the square of a Bernoulli random variable still a Bernoulli random variable?

2 votes
1 answer
53 views

How to prove that $E[U_1U_2 \mid |U_1-U_2|<a]$ is the sum of two double integrals?

2 votes
0 answers
69 views

If $X$ is standard normal, how to compute the PDF of $Y=X/(1+ e^{-X})$?

2 votes
1 answer
497 views

How to create a positive definite covariance matrix from an adjacency matrix?

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