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ki3i
  • Member for 9 years, 2 months
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23 votes

$\lim_{x\to0}\frac{e^x-1-x}{x^2}$ using only rules of algebra of limits.

10 votes
Accepted

Given $\mathbb{E}[X|Y] = Y$ a.s. and $\mathbb{E}[Y|X] = X$ a.s. show $X = Y$ a.s.

9 votes
Accepted

Random variables defined on the same probability space with different distributions

7 votes
Accepted

Asymptotic distribution for MLE of exponential distribution

6 votes

How to prove that $f: ℝ^n → ℝ^m$ is differentiable at $a$ iff each of its components $f_i$ is differentiable at $a$

6 votes

Prove that $a^2+b^2+c^2+3\sqrt[3]{a^2b^2c^2} \geq 2(ab+bc+ca).$

5 votes
Accepted

Problem with a trigonometric function: $\arctan ( \sin x /(1-\cos x))$

5 votes
Accepted

Compute the distribution of $\int_0^1 B_t dt$

5 votes
Accepted

Abstract Integration in Elementary Probability Theory

5 votes

Integrate in terms of t

5 votes

Computing quadratic variation and criteria for Brownian motion

4 votes
Accepted

Prove identity in law for stochastic process driven by Brownian Motion

4 votes
Accepted

Finding the inverse $(D - bb^T)^{-1}$

4 votes

Why is $\mathbb{P}(F\geqslant G) = \int_{\mathbb{R}} \mathbb{P}(F \geqslant g | G=g) \, D_G(g) \text{d}g$?

4 votes
Accepted

Ito's Integral's definition: Importance of isometry

4 votes
Accepted

Infinitesimal Random Variable

4 votes
Accepted

If $r<p<s$, then $||f||_p\le \max\{||f||_r,||f||_s\}$

4 votes
Accepted

Calculation of Radon–Nikodym derivative

4 votes
Accepted

Choosing exactly 2 damaged pieces (Probability)

4 votes
Accepted

Convergence in $L^1$ and uniform integrability

4 votes
Accepted

If $u\in L^1(0,1)$ is nonnegative and $E_n = \int_0^1 x^n u(x) \, dx$, prove $E_{n-k} E_k \leq E_0 E_n$.

4 votes
Accepted

Expectation of maximum of arithmetic means of i.i.d. exponential random variables

4 votes

How to find $\lim_{t\to0}\bigg(\int_0^1[bx+a(1-x)]^tdx\bigg)^{1/t}$

4 votes

How to derive the posterior predictive distribution?

3 votes
Accepted

Justifying a step in proving $M_{S\wedge T} = \mathbb{E}[M_T \mid \mathcal{F}_S ]$

3 votes
Accepted

Proving Conditional Probability Statement

3 votes
Accepted

What is the pdf and cdf of $aX^2+bX$?

3 votes

Evaluating a limit expression

3 votes

Proving finite sum identity

3 votes
Accepted

Convergence of a particular summation

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