Reputation
203,834
Next tag badge:
96/100 score
44/20 answers
Badges
17 145 323
Newest
 Revival
Impact
~2.0m people reached

10h
comment Find $\lim_{x\rightarrow\infty}\sin^2(x^2)$
Actually you might want to modify your post.
10h
comment Find $\lim_{x\rightarrow\infty}\sin^2(x^2)$
@TravisJ Why the strange edit?
10h
comment Find $\lim_{x\rightarrow\infty}\sin^2(x^2)$
Actually more or less trivial, by continuity of the sine function.
19h
comment limsup facts - which imply which?
No idea what a beast such as $$\bigcap_{n \geq 1} \bigcup_{m \geq n} X_n$$ can even mean.
19h
comment Expectation of an interval
$$Z=Y-X=\int_{X}^{Y}d\theta=\int_{-\infty}^{\infty}\mathbf 1_{X\leqslant\theta\leqslant Y}d\theta\implies E(Z)=\int_{-\infty}^{\infty}P(X\leqslant\theta\leqslant Y)d\theta$$
19h
comment Proposition on limsup
You misquote me again, please stop referring to sentences by others that you do not understand and ask your questions for themselves. Done deal?
20h
comment Determine if $(((13)),\circ)$ is a normal subgroup of $(S_{3},\circ)$
Now that the (rather ludicrous) notation problems are out of the way, this should be closed for lack of context.
22h
comment Distribution of Bernoulli and Uniform Random Variable
Of course P(X+Y=k)=0 for every k.
22h
comment Show $\limsup A_{2^n}$ is in the tail field.
Do you understand why the implication is false, or are you just admitting it is because somebody said so?
22h
comment Distribution of Bernoulli and Uniform Random Variable
"but could not get any further." Please explain why.
22h
comment Show $\limsup A_{2^n}$ is in the tail field.
"Without noting that $\limsup A_{2^n} \subseteq \limsup A_{n}$, prove $\limsup A_{2^n} \in \tau$." This seems to indicate that you believe that $B\subseteq C$ and $C\in\tau$ imply $B\in\tau$. If indeed this is so, you might want to reconsider.
1d
comment An application of Itô's lemma
You are right that the integral in (b) does not exist because $2t+B_t<0$ with positive probability. Are you sure about your source?
1d
comment How to show that the 3 events are independent but not pairwise independent
To be independent but not pairwise independent is impossible, please check your definitions.
1d
comment Probability and Integrals
@GeorgeS Please avoid minor edits on questions more than 4 years old (especially to edit incorrectly).
1d
comment Abel's summation formula for functions depending on limit of sum
Of course: fix $n$ and use Abel for the functions $f_n$ and $g$, where $f_n(x)=f(x,n)$.
1d
comment Sum of Gaussian and Binomial distribution
If $X$ is discrete with weights $(p_n)$, $Y$ absolutely continuous with density $f$, and $(X,Y)$ is independent, then $Z=X+Y$ has density $g$ where, for every $z$, $$g(z)=\sum_np_n\,f(z-n).$$ This is but the classical convolution of two probability measures, only here one is continuous and the other is discrete.
2d
comment Expected value of exponential random variable
$$E[X:A]=E[X\cdot\mathbf 1_A]=\int_AXdP.$$
2d
comment Total Differential / Ito dynamics
Use $M_t=e^{-t}N_t$ with $dN_t=e^{t}dS_t/S_t$ (by definition) and $dM_t=e^{-t}dN_t-e^{-t}N_tdt$ (Itô with $f(x,t)=e^{-t}x$) hence, indeed, $dM_t=dS_t/S_t-M_tdt$.
2d
comment Expected value of exponential random variable
"I'm not sure how to start here" By the definition: E[X|X<λ]=E[X:X<λ]/P[X<λ].
2d
comment Expectation of an Itô integral
This has been asked very recently. The simplest answer uses Itô's isometry, thus $$\mathbb{E}\left[W_T\cdot\int_{0}^{T} f(s)\cdot\mathrm{d}W_s\right]=\mathbb{E}\left[\int_{0}^{T}1\cdot\mathrm{d}W_s \cdot \int_{0}^{T}f(s)\cdot\mathrm{d}W_s\right]=\int_{0}^{T}1\cdot f(s)\,\mathrm ds.$$