# Tagged Questions

Use this tag only if your question is about the modern theoretical footing for probability, for example probability spaces, random variables, law of large numbers, and central limit theorems. Use [tag:probability] instead for specific problems and explicit computations. Use [tag:probability-...

61 views

### CLT question, the density function of the horizontal deviation from shot arrow to center is given…

The horizontal deviation from shot arrow to the center of the target is given as : $$\varphi (x)= \begin{cases} 1- |x| , x\in (-1,1) \\ 0 , \text{ otherwise. } \end{cases}$$ If the horizontal ...
23 views

### Is something wrong with my confidence interval for a Binomial variable?

Let $X$ be a Binomial random variable with parameters $n$ and $p$. I came up with the following very simple approach to finding a confidence interval for $p$, but the Wiki page on confidence intervals ...
19 views

50 views

### Maximise the integral w.r.t. probability measure.

Let $(Z_t)_{0\leq t\leq T}$ be a stochastic process. Then $Z_T$ is a r.v. and $F_{Z_T}$ a corresponding cdf. Suppose $\mathbb{E}[|e^{Z_t}|]<\infty$ for all $t\geq0$. Also \mathbb{...
130 views

### My proof that $S_n/\sqrt n$ does not converge in probability

I'm given a sequence $(X_n)$ of i.i.d. random variables with mean $0$ and finite variance $\sigma^2$. Let $S_n=X_1 + ... + X_n$. I have to show that $S_n/\sqrt n$ does not converge in probability. ...
103 views

### Origin of the notation for statistical divergence

The unusual notation $D(P||Q)$ seems to be universally used for statistical divergences (e.g. KL divergence). What is the origin of this notation, and do the double bars (pipe symbols) have any ...
19 views

42 views

### Autocorrelation function of a Wiener process & Poisson process.

Can anyone possibly explain step 3 and 4 in this solution?
34 views

### Markov chain: Find expected value to get back to starting state

I wonder why they complicate this solution? Call the mean time to get from i to j $M_{i,j}$ and set up three simple equations starting with $$M_{0,0} = 1 + (1/3)M_{1,0} + (1/3)M_{2,0}$$ and you get ...
41 views

### Expressing equal probability on an infinite line with probability axioms

Is there any way using the usual (Kolmogorov) axioms of probability to describe/model the following situation : A value $v \in \mathbb{R}$ has an equal probability of being measured anywhere in the ...
71 views

106 views

### What is a “continuous modification”? And can we always modify an almost surely continuous process, such that every path is continuous?

Let's motivate the question by a classical result: Let $(\Omega,\mathcal A,\operatorname P)$ be a probability space $\mathbb F=(\mathcal F_t)_{t\ge 0}$ be a filtration on $(\Omega,\mathcal A)$ which ...
53 views

A few days ago, I was introduced the concept of convergence in probability, after the almost sure convergence. I understood the almost sure convergence (I think): We have a sequence of random ...
Given $X_t=\int_0^t s W_s dW_s$ and the process $M_t=X_t^3-\int_0^t X_sY_s ds$. Find $Y_t$ such that $M_t$ is a martingale. I started thinking that $X_t$ can be seen as: $dX_t=tW_tdW_t$ then by ...
The following experiment is performed, Roll a dice. If you stick to the outcome, then the final score is the number on the dice. The experiment ends here. If the experiment is performed $n$ times, ...