Jerry West's user avatar
Jerry West's user avatar
Jerry West's user avatar
Jerry West
  • Member for 8 years, 7 months
  • Last seen more than 7 years ago
4 votes
1 answer
115 views

If $|z_1|=|z_2|=|z_3|$ and $\arg z_1\leq \arg z_2 \leq \arg z_3$ prove that $\arg{\frac{z_3-z_2}{z_3-z_1}}=\frac{1}{2}\arg \frac{z_2}{z_1}$

4 votes
3 answers
2k views

Find all the real solutions to the equation: $(x+i)^n-(x-i)^n=0$

3 votes
2 answers
61 views

How is $\sum_{k=0}^{\infty}\frac{e^{-1}}{(2k)!}=\frac{1+e^{-2}}{2}$

3 votes
2 answers
75 views

CLT question, the density function of the horizontal deviation from shot arrow to center is given....

3 votes
3 answers
88 views

Continuous function $f$ on $\mathbb R $ such that $f \notin L^1 (\mathbb R)$ but $f \in L^1([a,b]), a< b $

2 votes
1 answer
130 views

Inside a circle of radius $r$ insert a triangle with the largest possible area.

2 votes
2 answers
117 views

Conditional Extremes/Lagrange multipliers: proving: $\frac{1}{x_1}+...+\frac{1}{x_n} \geq \frac{n^2}{x_1+...+x_n}$

2 votes
1 answer
510 views

Inside an elliptical paraboloid with an equation $z=\frac{x^2}{a^2}+ \frac{y^2}{b^2}$ bounded by $z=h$ draw an right-angle parallelepiped..

2 votes
5 answers
90 views

Finding $\sum_{k=1}^{\infty}k^2 \frac{2^{k-1}}{3^k}$

2 votes
3 answers
74 views

Convergence of independent $\mathcal U {(n,n^2)}$ random variables?

2 votes
1 answer
1k views

Find the polynomial of the fifth degree with real coefficients such that...

1 vote
2 answers
92 views

Prove that $DX=E(D(X\mid Y))+D(E(X\mid Y))$

1 vote
1 answer
41 views

Finding the limit of $\lim_{x\to \infty}\frac{1}{10^x} \frac{1-e^{it}}{1-e^{\frac{t}{10}x}}=\frac{e^{it}-1}{it}$

1 vote
1 answer
317 views

Convergence of this set of random variables $Y_n$ where: $X_n: \mathcal U(0,1)$ independent random variables, $Y_n=\frac{1}{nX_n} n=1,2,...$

1 vote
0 answers
46 views

Questioning convergences in respect to $0$: almost surely, in probability, in distribution of random variable with $\varphi$ density given.

1 vote
1 answer
55 views

Using method of maximum likelihood find the estimator for $\mathcal N(m,1),m<0$ and $\mathcal U(\theta, 1), \theta<0$

1 vote
1 answer
508 views

Characteristic function of $X^2$ where $X: \mathcal N(0,1)$. $\int_{-\infty}^{+ \infty} e^{itx^2}\frac{1}{2 \pi}e^{-\frac{x^2}{2}}$dx?

1 vote
2 answers
172 views

Let $X_1,X_2,...$ be independent random variables each with expectation $\mu$ and $N$ a random variable that..

1 vote
3 answers
138 views

Definite integral $\int_{0}^{+ \infty}e^{itx}e^{-x} \frac{x^n}{n!}dx$

1 vote
1 answer
65 views

Finding the local extremes of this implicitly given function.

1 vote
1 answer
28 views

Drawing $D=\{(x,y)| |x-1|+|y-1|\leq \frac{1}{2}\}$ in $\mathbb R^2$

1 vote
2 answers
31 views

Find the extreme values of $f(x,y)=xy$ on $D=\{(x,y)|1 \leq x^2+y^2 \leq 4\}$

0 votes
1 answer
114 views

With the given point $M(a,b,c)$ in $\mathbb R^3$, find the tetrahedron with the smallest volume that is formed with a plane that..

0 votes
1 answer
32 views

Conditional Extreme. Find a point in $\mathbb{R^2}$ that has the smallest sum of squared distances from the lines $x=0,y=0, x-y+1=0.$

0 votes
1 answer
99 views

Proving that $c_c(\mathbb N)$ is a dense subset of $l^p(\mathbb N)$

0 votes
2 answers
68 views

A function that maps $R^m \to R^n$ where, $m<n$ is called?

0 votes
1 answer
110 views

Proving that $l_r$ is dense everywhere in $l_p$ $1\leq r \leq p$

0 votes
1 answer
55 views

Relational Aglebra, dont know what to do!

0 votes
1 answer
56 views

If $E,F \in \mathcal L \implies E \bigcap F \in \mathcal L $ Caratheodory condition of measurability.

0 votes
2 answers
486 views

Solving these types of integrals, using Monotone convergence theorem and Dominated convergence theorem.