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Results tagged with probability-distributions
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user 81488
In probability and statistics, a probability distribution assigns a probability to each measurable subset of the possible outcomes of a random experiment, survey, or procedure of statistical inference.
4
votes
Slight variation on law of the iterated logarithm
You can use the fact that $B_t-m_t$ is a reflected Brownian motion (see e.g. Revuz-Yor, Chapter VI, Theorem 2.3). I think it shouldn't be difficult to show that
$$
\limsup_{t\to\infty} \frac{M_t-m_t}{ …
- 1,897
4
votes
Counterexample: weak convergence doesn't imply $L^1-$convergence
If, for $n>2$, $\mu_n$ puts masses $n^{-1},n^{-1}, 1-2n^{-1}$ at $2n, -n, -\frac{n}{n-2}$ respectively (so that $\mu$ puts the unit mass at $-1$), doesn't it work?
- 1,897
2
votes
Accepted
Conditioned binomial dominates unconditioned with different parameter
This does not seem to be true. Take $p=2/3$ and $n=k=1000$. Then, you need that
$$
\frac{(2/3)^{1000}}{1-(1/3)^{1000}} \geq (2/3)^{999},
$$
which is clearly false.
- 1,897
2
votes
Accepted
CLT for Bernoulli RV with negative correlation
No, the CLT need not hold under these assumptions. Consider the following example: take $p=1/2$ for definiteness, and divide the (discrete) time into intervals $I_1=[1,2]$, $I_n=(2^{n-1}, 2^n]$, $n\ge …
- 1,897
0
votes
A question in central limit theorem
Doesn't it follow from the Lévy's continuity theorem? I mean, consider the characteristic functions of $S_{n-1}/s_n$ and $X_n/s_n$, the product of them converges to $e^{-t^2/2}$, so the characteristic …
- 1,897