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$t^5 - 6t + 3 = 0$


1d
reviewed Approve Proof of expression with integrals
1d
answered probability of a brownian motion being equal to the running maximum
2d
reviewed Approve Speed of light and relativity
2d
awarded  Constituent
2d
revised $G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$
added 106 characters in body
2d
comment $G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$
@user3018 I don't know other sources. I know this method when once answering a question on this site. Sorry I didn't notice that $\mu\neq 0$, then some modification is needed. See in the reference how the second order delta method is roughly proved, you can easily modify my answer(probably by replacing the $\chi_1^2$ by something else.) But the idea of this solution still works
2d
comment $G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$
@user3018 yeah you can add the negative sign, it doesn't change the steps. For the last step, you can suppose the convergence to $0$ is not true then get a contradiction with the statement before last. How to define $g(X_n)$ when $X_n=0$ does not matter, you can define it in the same way as you define $X_n^{-1}$
2d
revised $G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$
edited title
2d
answered $G_n:=\sqrt{n} \left(X_n-1\right) \xrightarrow[n]{d} N(\mu,\sigma^2) $ implies $\sqrt{n} \left(1-X_n^{-1}\right)=G_n+o_P(1)$
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awarded  Enlightened
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awarded  Nice Answer
Dec
18
comment Show that $\{e^{in}: n\in\Bbb N\}$ is Dense in the Unit Circle
Try to use Pigeonhole principle
Dec
18
answered $|p(z)| \leq M$ for $|z| \leq 1$ Show that $|p(z)| \leq M|z|^n$ for $|z| \geq 1$
Dec
16
comment Brownian brigde, brownian motion and independence.
replace $B_t$ by $W_t -tW_1$, then make direct computation. Notice that $EW_tW_s = s\wedge t$
Dec
16
reviewed Approve Is the empty set internal?
Dec
16
comment A set of 19 numbers that are at most 93, and a set of 93 numbers that are at most 19, have equal sumsets
Why is this question closed?
Dec
15
reviewed Approve Finding a limit using change of variable- how come it works?
Dec
15
reviewed Approve Equivalence between the GNS representation of two different positive linear functionals
Dec
14
comment Compute almost sure limit of martingale?
@Bob I've made an answer
Dec
14
answered Compute almost sure limit of martingale?