2,574 reputation
2826
bio website google.com
location Ames
age 33
visits member for 1 years, 7 months
seen Apr 10 at 22:01

I am Patrick.


Jan
21
awarded  Notable Question
Dec
17
awarded  Popular Question
Sep
30
comment Prove that $\frac{n!}{(n-k)!} = n^{\underline{k}}$
The definition can be found here.
Sep
25
awarded  Yearling
Sep
21
comment $n!\sum_{k=1}^n \frac{a_{k}}{k!}$ is always integer.
$n!/k! = n(n-1)\cdots(n-k+1)$ is always integer.
Sep
18
comment Word and Latex: Probability
Your thought on (a) is not correct.
Sep
12
comment Expressing $A \cup B \cup C$ as a union of mutually exclusive events
If you draw a Venn diagram, it will be easier.
Sep
12
revised Is this correct method to prove that $a^2 + b^2 + c^2 ≥ ab + bc + ac$, when $a,b,c \geq 0$?
added 16 characters in body; edited title
Aug
23
awarded  Popular Question
Jul
23
revised Probability and sets
added 83 characters in body
Jul
6
comment How to find the $x^2+y^2=?$
$x$ and $y$ can be real too, for example, x -> -0.161586, y -> 1.16159
Jul
6
comment How to find the $x^2+y^2=?$
OP, so $x$ and $y$ are allowed to be complex numbers?
Jul
2
revised Normal distribution inequality
added 1 characters in body
Jul
2
revised Given that the first child draws $10\$$ from his envelope, what is the probability that the second child has an envelope that contains a 20$ note?
edited title
Jun
26
revised estimate the population numbers
added 12 characters in body
Jun
26
revised How many arrangements of a (generalized) deck of (generalised) cards have pairs in them?
latex updated
Jun
25
awarded  Great Answer
Jun
15
comment $3^{3n+1} < 2^{5n+6} $ for all non-negative integers $n$. Is my induction solution correct?
Looks good. But what does $P(0)=T$ mean?
Jun
9
comment Limit of $\cos(x)/x$ as $x$ approaches $0$
I would pick an arbitrary large number $N$, and show that whenever $x$ is less than a threshold value, $\cos(x)/x > N$.
May
24
comment Upper and Lower Triangular Matrices
Find a lower triangular matrix $L_{4\times 4}$ and a upper triangular matrix $U_{4\times 4}$ such that $A=L_{4\times 4} U_{4 \times 4}$.