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Fnacool
  • Member for 8 years, 3 months
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31 votes
Accepted

How to prove that $ {\mathbf{GL}_{n}}(\mathbb{R}) $ is dense in $ {\mathbf{M}_{n}}(\mathbb{R}) $

10 votes
Accepted

Prove that $f(1999)=1999$

10 votes
Accepted

Uniform and Pointwise convergence Almost Everywhere

8 votes
Accepted

Evaluation of $\sum^{\infty}_{n=0}\frac{1}{16^n}\binom{2n}{n}.$

7 votes

Suppose that $E[X^n] = 3n$. Find $E[e^X]$...

7 votes

If $x+\frac{1}{x}=\frac{1+\sqrt{5}}{2}$ then $x^{2000}+\frac{1}{x^{2000}}= $?

7 votes
Accepted

Approximating Borel Measure with Atomic Measures

7 votes
Accepted

Tightness + Integrability does not imply uniform integrability?

7 votes

Durret 2.5.8: Question about probability of limsup

6 votes

If $\int_a^bg(x)dx=0$, show that $\int_a^bf(x)g(x)dx=0.$

6 votes
Accepted

An example to show that direct product is not necessarily cancellative for infinite groups.

5 votes
Accepted

Why cadlag Processes have atmost countable discontinuities?

5 votes
Accepted

convergence in distribution of exponential of a brownian motion

5 votes

Graph of a continuous function has measure zero

5 votes
Accepted

$|f′(x)| \leq c|f(x)|$ for all $x \in (0,1)$ and $f(0)=0$. Show that $f(x) = 0$ for all $x \in [0,1]$.

5 votes
Accepted

$\sum_n \int_{A_n} |f(x)| d\mu < \infty $

5 votes
Accepted

If $X_n$ converge to a negative number in probability, then $\lim P(X_n > 0) = 0$?

4 votes
Accepted

how to find $\frac{d}{dx}\left( \int_0^x f(x,t)dt\right)$?

4 votes
Accepted

Probability from randomized dice

4 votes

Proving $(n+1)$th differential is $0$ given lower differentials are $0$

4 votes
Accepted

Evaluating $\lim\limits_{n \to \infty} \sqrt[n]{\frac{n!}{\sum\limits_{m=1}^n m^m}}$

4 votes
Accepted

If $\frac{1}{n} \sum_{i=1}^n X_i$ converges a.s. to a finite constant, then $E|X_n|<+\infty$.

4 votes

Random Walk of a drunk man

4 votes
Accepted

Cars in Traffic

4 votes

Uniform Integrability of Random Variables

4 votes

Can we claim that all the terms in a matrix are less than equal to 1 if spectral radius is less than 1?

4 votes

Eigenvalues are measurable

4 votes
Accepted

Sequence of Measurable Sets Converge Pointwise to a Measurable Set

4 votes
Accepted

Gaussian random variables independent iff statement

4 votes
Accepted

Is the right-hand derivative equal to the right-hand limit of the derivative?

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