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1d
awarded  Constituent
2d
comment $\mathbb E[\bar X_n]=0$
aka the tower property for conditional expectations.
Dec
14
comment $X:\Omega \to \mathbb{N}$ is random variable, How to prove that $E[x]=\sum_{i} \Pr(X\ge i)$?
@BCLC: Yes, Lebesgue integral over $\mathbb{N}$ with respect to the counting measure yields infinite sums. That you may interchange the order of double-sums when the summands are non-negative follows immediately by the non-negative version of Fubini (which is usually called Tonelli's theorem).
Dec
14
comment $X:\Omega \to \mathbb{N}$ is random variable, How to prove that $E[x]=\sum_{i} \Pr(X\ge i)$?
@BCLC: Sums are integrals with respect to the counting measure.
Dec
14
comment If $E[X(t)X(s)]=t \land s $. Show that this process has independent increments
Personal input, please.
Dec
13
comment Probability and stuff
Show some personal input and stuff.
Dec
13
comment $X:\Omega \to \mathbb{N}$ is random variable, How to prove that $E[x]=\sum_{i} \Pr(X\ge i)$?
This has been asked several times already. Try and search the site. (Side note: $\sum_{x\in\Omega} P(X=x)$ doesn't make sense, since $X$ takes values in $\mathbb{N}$, not $\Omega$).
Dec
12
comment Finding the Cumulative Distribution Function
Because $F_X(x)=\int_{-\infty}^x f_X(t)\,\mathrm dt$ which is $\int_{-1}^0 (-t)\,\mathrm dt +\int_0^x t\,\mathrm dt$ for $0\leqslant x\leqslant 1$.
Dec
10
comment Notation for Markov Model
This is most likely explained in the book you're following.
Dec
10
comment Reconciling two different concepts of conditional probability
Got anything from the answer below?
Dec
9
awarded  Caucus
Dec
8
comment Show that $E(X)=\sum_{n\in\mathbb{N}}P(X\ge n)$
Integrate the pointwise equality $X=\sum_{n\in\mathbb{N}} \mathbf{1}_{X\geqslant n}$ and use Tonelli to interchange sum and integration.
Dec
8
comment IId random variables from Exponential distribution
What have you tried?
Dec
5
comment If $X$ and $Y$ are independent random variables, does it follow that $X^2$ and $Y$ are independent?
Any function of $X$ is independent of any function of $Y$.
Dec
5
revised Is $e^{2(\cos(t)-1)}$ the characteristic function of some random variable?
added 1 character in body
Dec
4
comment Student's distibution
What does "$n$-th" refer to here? The number of degrees of freedom?
Dec
3
revised What is the joint distribution of these two obscured exponential ones?
edited body
Dec
2
revised A basic measure theory question on lebesgue integral
added 21 characters in body
Dec
2
answered A basic measure theory question on lebesgue integral
Dec
2
comment A basic measure theory question on lebesgue integral
Are $\mu$ and $\nu$ Borel probability measures, i.e. probability measures defined on the sigma-algebra generated by the open sets?