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Math-fun
  • Member for 7 years, 7 months
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10 votes

Memoryless property and geometric distribution

10 votes

How many ways can seven people sit around a circular table?

9 votes

Compute $\int_{0}^{1} \frac{\ln(x)}{(x+1)^2} \mathrm dx$

8 votes
Accepted

Series Approximation How to evaluate $1/3+1/3(1/3)^3+1/5(1/3)^5+...$?

8 votes
Accepted

Evaluate $\int_0^1 \frac{\log(1+x)}{x}$

8 votes

Why aren't the functions $f(x) = \frac{x-1}{x-1}$ and $f(x) = 1$ the same?

8 votes

How did Euler realize $x^4-4x^3+2x^2+4x+4=(x^2-(2+\alpha)x+1+\sqrt{7}+\alpha)(x^2-(2-\alpha)x+1+\sqrt{7}-\alpha)$?

8 votes

Proof of a Ramanujan Integral

8 votes

I am trying to maximize an exponential function

8 votes

Why is $\int_0^{2\pi}{\sin x\over x}$ bigger than 0?

8 votes
Accepted

If $\lim_{n\to\infty}\frac{1^a+2^a+...+n^a}{(n+1)^{a-1}.((na+1)+(na+2)+...+(na+n))}=\frac{1}{60}$, Find the value of a

8 votes
Accepted

Finding $\lim_{n\to \infty}\frac{1}{n^2}\left(e^{1/n^2}+2e^{2^2/n^2}+\cdots+ne^{n^2/n^2}\right)$

7 votes
Accepted

Help to prove that : $\int_{0}^{1}\int_{0}^{1}{1-x\over 1-xy}\cdot{x\over \ln{(xy)}}dxdy={1\over 2}\ln{1\over 2}$

7 votes
Accepted

$\lim_{n\to\infty }n\sin (\frac{1}{n^{2}+1})$

7 votes
Accepted

How to calculate \sqrt{7+2\sqrt{10} } =

7 votes

what is the expected value of $x^TAx$?

6 votes

What is the appropriate method to find the value of $1$ - $1\over 7$ + $1\over 13$ - ... upto infinite terms?

6 votes

Prove that $E(X) = \int_{0}^{\infty} P(X>x)\,dx = \int_{0}^{\infty} (1-F_X(x))\,dx$.

6 votes
Accepted

Evaluate the sum $\sum_{n=0}^\infty \frac{x^{2n+1}}{(2n+1)!}$

6 votes

Negative binomial distribution - sum of two random variables

6 votes

Evaluation of $\int_0^1 \frac{x^3}{2(2-x^2)(1+x^2) + 3\sqrt{(2-x^2)(1+x^2)}}\,\mathrm dx$

6 votes
Accepted

Solve the system $x^2-3xy+2y^2+x-y=0$, $2x^2-2xy-3y^2-2x+5y=0$

5 votes

Prove that, $(2\cdot 4 \cdot 6 \cdot ... \cdot 4000)-(1\cdot 3 \cdot 5 \cdot ...\cdot 3999)$ is a multiple of $2001$

5 votes

Implementing Ornstein–Uhlenbeck in Matlab

5 votes
Accepted

Is there another simple way to solve this integral $I=\int\frac{\sin{x}}{\sin{x}+\cos{x}}dx$?

5 votes

Solving for n in the equation $\left ( \frac{1}{2} \right )^{n}+\left ( \frac{1}{4} \right )^{n}+\left ( \frac{3}{4} \right )^{n}=1$

5 votes
Accepted

deriving mean & variance for poisson using mgf

5 votes
Accepted

$\int\limits_{0}^{\pi/2}\frac{1+2\cos x}{(2+\cos x)^2}dx$

5 votes

Other ways to evaluate the integral $\int_{-\infty}^{\infty} \frac{1}{1+x^{2}} \, dx$?

4 votes

How to solve the trigonometric equation $\sin x-\cos x-2(2)^{\frac 1 2}\sin x\cos x=0$

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