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11h
comment Show that $\min_K f$ exist.
Try intersecting $K$ with a suitable ball.
11h
comment Showing that $(X_n)$ obeys the Markov Property.
Is this a PSQ or what?
11h
comment $f$ is continuous, $f : X \to X$, $X$ compact, and $f$ has an $\epsilon$-fixed point for each $\epsilon > 0$. Show $f$ has a fixed point.
Hint: Every sequence in a compact set has a converging $______$.
11h
comment Show that $\min_K f$ exist.
Hint: Find a compact set in the picture.
11h
comment Is there an easy proof that the set of $x \in [0,1]$ whose limit of proportion of 1's in binary expansion of $x$ does not exist has measure zero?
The "fact" you want to use does not seem obvious. Strong law of large numbers, on the other hand...
12h
comment pascal's triangle sum of nth diagonal row
Then the relation ${i\choose j}+{i\choose j+1}={i+1\choose j+1}$ is all one needs to prove this by induction.
12h
comment absolute value binomial split into two absolute values
Or if $a\leqslant b\leqslant0$.
12h
comment pascal's triangle sum of nth diagonal row
What is $P_r$, already?
13h
comment intuition of mass function of random variable
$f(x)=$ size of $\{X\leq x\}$? Certainly not.
13h
comment Taylor Series for $\frac{1}{ 1+x+x^2}$
Your approach yields a series in $t= \frac {2x+1}{\sqrt 3}$ while you are asked a series in $x$. The answer is the series $\sum\limits_na_nx^n$ where $a_{3n}=1$, $a_{3n+1}=-1$ and $a_{3n+2}=0$ for every $n\geqslant0$.
13h
comment Limit of a recurrence
@Julián Is it not? Why?
16h
comment Help needed to solve probability problem
Hint: One throws a coin three times with probability h for head and t=1-h for tails, what is the probability to obtain one head and two tails?
16h
comment Properties of independence and conditional independence
Please show your solution to 1 and your tries to 2 and 3.
19h
revised Properties of independence and conditional independence
edited title
19h
comment Properties of independence and conditional independence
These are direct consequences of the definitions, for example $X\perp A\mid B$ and $X\perp B$ means that $P(X=x,A=a\mid B=b)=P(X=x\mid B=b)P(A=a\mid B=b)$ and that $P(X=x,B=b)=P(X=x)P(B=b)$ for every $(x,a,b)$, hence...
19h
revised Show that $\lim\limits_{n\to\infty}\frac1{n}\sum\limits_{k=1}^{\infty}\left\lfloor\frac{n}{3^k}\right\rfloor=\frac{1}{2}$
deleted 18 characters in body; edited title
19h
comment Is the sudden appearance of transient random walks in 3-dimensions a phase transition?
And now you seem to embark us onto a quite different question...
19h
comment Asymptotic probability that two integers are coprime
...Assuming that divisibilities by different primes are independent events--which is kind of the main part of the proof.
22h
comment How to deduce this fact from the existence of factorized regular conditional probabilities and disintegration of probability measures?
Indeed, by the definition (1), $$\mu(S\times B)=\iint_{S\times B}\mathrm d\mu(x,y)=\iint_{S\times B}p(x,\mathrm dy)\mathrm d\mu_1(x)=\int_S\int_Bp(x,\mathrm dy)\mathrm d\mu_1(x)=\int_Sp(x,B)\mathrm d\mu_1(x).$$
22h
comment hitting times and stopping times
"stopping times are always hitting times" No. Hitting times are always stopping times but lots of stopping times are not hitting times. "Last exit times are not stopping times" True, nobody says they are, and they are not hitting times either.