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Apr
29
comment Probability Game
Based on the show, $Asp=Bsp=1$
Apr
27
comment why is variance so famous that it appears in almost half of the probability textbook?
What is this other half of textbook I haven't heard of?
Apr
26
comment Understanding $P(X=n)=0$ when $X$ follows a continuous distribution
An event having probability zero doesn't mean that it is impossible, more that it will almost never occur. Repeat your experiment and you should almost never get that particular number $n$ again.
Apr
19
comment infinite sum limit how to find the following
You probably mean $k/n$.
Apr
17
comment Does there exist a finite fair gamble game with one dishonest coin?
No problem, you accept whatever answers you want, and can upvote as many as you wish. Happy to have been helpful
Apr
17
revised Does there exist a finite fair gamble game with one dishonest coin?
deleted 44 characters in body
Apr
17
comment Does there exist a finite fair gamble game with one dishonest coin?
It will depend on what is fixed. If you fix $N$ and have the liberty to choose the coin, then yes you can, as my answer shows. However if you have the coin at your disposition and must find $N$, it might not be possible, as shown by Ross.
Apr
17
comment Does there exist a finite fair gamble game with one dishonest coin?
@jonathan Rich The answer provided by Ross shows that for certain $p$ it can be impossible to do. I take any $N$ and show that you can find a $p$.
Apr
17
revised Does there exist a finite fair gamble game with one dishonest coin?
added 295 characters in body
Apr
17
answered Does there exist a finite fair gamble game with one dishonest coin?
Apr
13
answered Independence between Uniform distribution and Exponential distribution question
Apr
9
awarded  Nice Answer
Mar
23
comment This population will be extinct or not
One can show that almost surely, there will be extinction of the population if the mean of the reproduction distribution is less than or equal to $1$, provided $0$ child is possible. Unfortunately i can't type the proof, but it has to do with fixed point of the generating function of the reproduction law. See for example cims.nyu.edu/~csplash/data/notes/2011-24.pdf
Mar
23
comment This population will be extinct or not
This is a special case of branching process, look out this question for some insight: math.stackexchange.com/questions/295353/branching-process
Mar
20
comment $\int \frac{x^3}{\sqrt{2 -x}}dx , \int \cosh^2(x)dx ,\int \frac{x^2 + 1}{x^2 + 2x + 2}dx$
I think you should be having $\cosh(x)\sinh(x)$ in your integration by parts. Also you can use directly $u=\sqrt{2-x}$ to take care of the root in the first one but that is just preference.
Mar
11
comment Random Walk probability game
That is good to know!
Mar
11
comment Random Walk probability game
@joriki There should be a search function inside our past answers
Mar
11
comment Random Walk probability game
@joriki That was me being lazy to type the argument, googling for it instead
Mar
11
comment Random Walk probability game
This might help math.stackexchange.com/questions/116446/random-walk-on-n-cycle
Mar
4
comment Which is bigger $(n!)^m$ or $(m!)^n$?
Which is bigger, $n$ or $m$?