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Jul
26
comment Expected maximum degree Erdős–Rényi graph
I believe you can do more than that. Once the degree of each vertex follows a binomial distribution of parameters $N-1$ and $p$, via Chernoff bounds you can assure that every vertex is close to his expected value. Then, the maximum degree will be close of $(N-1)p$ with high probability.
Jul
9
comment Using Mathematica to calculate expected time to absorption
I got it. You want to solve the recurrence relation. Maybe the Mathematica's stack would be more useful.
Jul
9
comment Using Mathematica to calculate expected time to absorption
Are you interested to obtain the script written in Mathematica language or the algorithm? If is the second, you could fix $n$, simulate the process many times. This would give you an idea of ETA for the $n$ fixed. Then you could do the same to others values of $n$ and do interpolation to try to find the right curve...
Jun
24
revised Is my answer correct? Expected number of coin flips to get 5 consecutive heads
added 55 characters in body
Jun
24
comment Is my answer correct? Expected number of coin flips to get 5 consecutive heads
Thanks! you too.
Jun
24
comment Is my answer correct? Expected number of coin flips to get 5 consecutive heads
Well, I see this kind of solution, usually, in problems involving Discrete Markov Chains. The Gambler's ruin, the first run of three sixes, the secretary problem are classical problems of the subject.
Jun
24
comment Is my answer correct? Expected number of coin flips to get 5 consecutive heads
No problem, it isn't my first language too. Well, now I get it. And it is correct.
Jun
24
answered Is my answer correct? Expected number of coin flips to get 5 consecutive heads
Jun
24
comment Is my answer correct? Expected number of coin flips to get 5 consecutive heads
I tried to understand the definition of your $X_i$ but I failed. Could you explain again? I didi't understand what you meant by "probability of the random variable $X_i$."
Jun
19
answered What is $\lim_{x\to 0} \sum_{n=2}^\infty \frac{\sqrt{x}\ln n}{1+n^2 x}$?
Jun
17
comment Convergence in distribution with finite mean
Unfortunately, it is wrong. If you simply take $X=Y$ in distribution you have that all the means are equals, thus you have convergence for the sequence they form.
Jun
12
answered Degree distribution of the line graph of an Erdös-Rényi random graph
Jun
5
answered Cebîsev Inequality or Central limit Theorem
Apr
13
revised Could we define two random variables such that the product of them is Normal distribution(Gaussian)?
improved formatting
Apr
13
suggested approved edit on Could we define two random variables such that the product of them is Normal distribution(Gaussian)?
Apr
3
revised Conditional Probability in Geometric Distribution
improved formatting
Apr
3
suggested approved edit on Conditional Probability in Geometric Distribution
Apr
1
comment If $\mu$ is $f$-invariant for a collection generating the Borel $\sigma$-algebra, then $\mu$ is $f$-invariant?
Try to define $\mathcal{C}_{\epsilon} = \{ C : \| \mu(A) - \mu (f^{-1}(A)) \| < \epsilon\}$
Apr
1
comment If $\mu$ is $f$-invariant for a collection generating the Borel $\sigma$-algebra, then $\mu$ is $f$-invariant?
The family $\mathcal{C}$ is clearly a $\lambda$-system. You could try the $\pi - \lambda$-theorem.
Apr
1
comment If $\mu$ is $f$-invariant for a collection generating the Borel $\sigma$-algebra, then $\mu$ is $f$-invariant?
I guess this is general, but if $\mu$ is a finite measure you can play with the fact that $f^{-1}$ behaves very well under sets operations. From that you can have that $\mathcal{C}$ is in fact an algebra. Maybe there is a way to avoid the sets with infinity measure...