Questions on using, finding, or otherwise relating to probability distributions, pdfs, cdfs, or the like.

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2
votes
0answers
101 views
+50

Find a probability density

I am going through a paper trying to understand all the single steps, but I got stuck. I need to calculate $$p(x+\delta t) \mid x(t), t)= \int p(x(t+\delta t) \mid \mu , x(t), t)p(\mu\mid x(t), t) ...
2
votes
0answers
54 views
+50

Solution to a certain moment problem

I'm looking for a function $f$ that satisfies $f(x)\geq0$ $\int f(x) \mathrm{d}x=1$ $\int xf(x) \mathrm{d}x=0$ $\int x^2f(x)\mathrm{d}x=1$ $\int x^4f(x)\mathrm{d}x=\delta$ $\int ...
6
votes
1answer
69 views
+100

Multivariate normal density function of function of random variable

Let $X_1,\dots,X_n$ be i.i.d random variables and $g$ be a symmetric function such that $$g(X_i,X_j)\sim N(\mu,\sigma^2)$$ for all $1\le i<j\le n$. I wish to know the density function of the joint ...
1
vote
0answers
18 views
+200

Lower bound for (function of) density of well-behaved random variable

Suppose we have a non-negative random variable $\tilde{\theta}$ such that $\mathbb{E}\tilde{\theta} = a > 0$, with finite variance $\sigma^2$. $\tilde{\theta}$ can take on values from $0$ to ...
3
votes
1answer
83 views
+50

Warren's proof for Benford's Law

Warren has a little proof of Benford's law in Hacker's Delight. To quote: Let $f(x)$ for $1 \leq x < 10$ be the probability density function for the leading digits of the set of numbers with ...