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age 30
visits member for 2 years, 7 months
seen 13 hours ago

Likes: Java, Android, iPhone, Python, Linux Ubuntu and Mint, Eclipse, C, graphic design, Mathematics, foreign languages, hopefully Go when I get round to learning it...


Jul
13
accepted Quaternion Group as Permutation Group
Jul
13
asked Quaternion Group as Permutation Group
Jun
3
awarded  Yearling
Mar
11
awarded  Popular Question
Jan
30
comment Nonlinear Second Order Differential Equation
Wow. So simple. I feel stupid.
Jan
30
accepted Nonlinear Second Order Differential Equation
Jan
30
asked Nonlinear Second Order Differential Equation
Jan
16
awarded  Nice Question
Jan
9
comment Taking balls from a bag with replacement
Oh, thanks. Never heard of this problem, so it was difficult to google it.
Jan
9
asked Taking balls from a bag with replacement
Aug
17
awarded  Supporter
Aug
17
accepted Modern formula for calculating Riemann Zeta Function
Aug
17
asked Modern formula for calculating Riemann Zeta Function
Dec
30
revised Probability and the Collatz Problem
added 561 characters in body
Dec
30
comment Probability and the Collatz Problem
I would like to offer a thought experiment: If you pick one thousand positive even integers randomly and do one iteration, $C(n)$ of each, then on average, half the results will be even. If you do this again $C^{2}(n)$ then 5/8 will be even, and so on. As you keep going, I think you will find that the average settles at 2/3. I don't think Chebyshev's inequality matters, as that is asking a different question.
Dec
30
revised Probability and the Collatz Problem
added 1741 characters in body
Dec
30
revised Probability and the Collatz Problem
edited body
Dec
30
comment Probability and the Collatz Problem
@Alex Becker I don't think the probability $C^{k}(n)$ is even depends on anything other than the fact that $n$ is even (and positive). The probability tree takes into account all possible paths the Collatz iterations have on $n$, so the probability is just the sum of all paths that end in a positive number, which can be found with a geometric sum.
Dec
30
comment Probability and the Collatz Problem
@Roupam Ghosh. We only need assume $n$ is even. All possible paths (e.g. even, odd, even,even,even,odd...) are accounted for when caclulating the probability that $C^{k}(n)$ is even.
Dec
30
comment Probability and the Collatz Problem
@Roupam Ghosh - yes the last few lines were a bit of a fudge. When I wrote this out properly years ago I had a slightly stronger way of arguing it. I've forgotten it though...