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Aug
22
awarded  Quorum
Aug
22
comment There are finitely many maps on nonnegative integers satisfying $\phi(ab)=\phi(a)+\phi(b)$
The number is infinite if you change the domain to $\mathbb{N}$. Use logs with arbitrary bases.
Aug
6
answered Transforming discrete R.V. to uniform R.V.
Jun
24
awarded  Citizen Patrol
Apr
17
comment Count no. Of ways
You might find reading about the 12 fold way helpful: en.wikipedia.org/wiki/Twelvefold_way
Apr
15
comment Count no. Of ways
Presumably the OP meant boxes that are indistinguishable from one another. Your answer assumes the boxes are distinguishable (i.e. labelled).
Apr
3
comment Does $\sin(\sin(\sin\cdots(\sin1)\cdots) \rightarrow 0 $?
Hint: what solutions are there to the equation x = sin(x)
Feb
24
comment How to solve this recurrence $T(n)=2T(n/2)+n/\log n$
is T evaluated at floor(n/2)? ceiling(n/2)? Or do you assume n is always a power of 2?
Jan
17
comment Ergodic Process: Does it visit all state?
@triomphe Silly example, $X(t) = B(t) + e^{-t}$ where $B(t)$ is a brownian motion, is ergodic, but not stationary.
Jan
17
comment Ergodic Process: Does it visit all state?
There's no relationship between stationary and ergodic. They are different attributes of processes. If a process has both attributes, you can prove a lot of theorems about the process.
Jan
14
comment Splitting a sandwich and not feeling deceived
@user1729 then your boss is not an engineer. He just thinks he is.
Jan
3
comment Task from Probability
What distribution are you using to "randomly select" the real numbers?
Jan
3
comment random circle with radius r on cartesian plane, probability of it not cutting x and y axis with intercepts.
Please define "put" more clearly. How is this disk "put" onto the plane?
Dec
20
answered Prove a given sequence of real numbers is convergent
Dec
20
comment Prove a given sequence of real numbers is convergent
To show that $y_n$ is convergent, focus on the properties of $y_n$. There are several facts about $y_n$ that you should be able to deduce directly from your above statements. Do those facts help you to prove convergence?
Dec
11
answered Ways to put $n$ balls into $m$ boxes
Dec
11
comment Ways to put $n$ balls into $m$ boxes
These are 4 of the 12 problems in "the twelvefold way": en.wikipedia.org/wiki/Twelvefold_way
Dec
9
comment PDF and CDF of the division of two Random variables
I hadn't seen @fgp's comment when I wrote this, which is essentially identical. Funny we both chose 1K samples.
Dec
9
answered PDF and CDF of the division of two Random variables
Dec
9
comment solving a hardcore limit with product
Write down the summation you get from 2. Look at it, and realize that the summation looks like f(k/n x) where k is ranging from 0 to n-1, that's a Riemann Sum, and for a well behaved function (which cos is) converges to the integral.