# 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-...

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### Interpretation of measure theory question

I am struggling with the following question: Let $\Omega = \{1,2,3,4\}$, $\mathscr E = \{\{1\}\{1,2\}\}$ (a) Find $\sigma (\mathscr E)$ (sigma algebra) (b) By inventing an analog of a pmf or cdf, ...
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### Convergence of derivative in $L^1(\mathbb R)$

Let $F(x)$ be a distribution function over $\mathbb{R}$ with positive derivative at origin $f(0)$. Let $Q$ be a measure on $\mathcal{B}(\mathbb{R})$. Can we have following results under some ...
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### How can I can calculate the CDF of the random variable?

Assuming that $H$, $N$ are random variables in which $H$ is distributed following exponential distribution with mean value $\Omega$, and $N$ is a Gaussian random variable with probability density ...
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### Existence of a Continuous Modification of Fractional Brownian Motion

For a course on stochastic processes, I've been working on an exercise on fractional Brownian Motion. Showing that this process has a continuous modification is one of the final steps of the exercise, ...
Let $\{X_i \}^\infty_1$ be independent random variables (that is, any finitely numbers of random variables are independent). Furthermore, if $S_n=\sum_1^n X_i$ converges almost surely to a random ...