Recent content by vladb

Wow, you brought this up after a year? Interesting :) But anyway, the definition of 'random string' I used in my claim is just a random variable that is represented as a string, where each character is chosen independently and uniformly at random. Its entropy is just the entropy of this random...

Try to calculate the derivatives more carefully, because what you stated is false. The first term is not the only non-zero term (there are infinitely many non-zero terms). The chain rules gives a correct result. (perhaps you are forgetting about the product rule)

How exactly did you get 110.2 bits? The fact that you gave entropy for a piece of english text shows that you somewhat misunderstand entropy/information theory. In fact, no one knows exactly the entropy of english text (it doesn't even make much sense). On the other hand, we can exactly...

Maybe somewhat off-topic, but it always made me wonder, why do people keep saying actuarial work is so boring (especially with such assurance and strong words)? Where does this information come from? To me it seems it's the typical unsupported "internet advice", that gets blindly passed from...

What type of series are you interested in? Taylor? You can use wolframalpha's symbolic calculator: http://www.wolframalpha.com/input/?i=series+b+%2B+m%2F%281%2Bexp%28H-x%2Fr%29%29

I agree with chiro's advice, but would like to note that actuarial science is not only about insurance, although it is indeed the most typical application. Actuaries also work in banks and other financial institutions (e.g. FSA or investments/risk management department of a large any-sector...

I'll add that in non-parametric statistics we can have specific distribution assumptions, but indeed it's probably less often. Also non-parametric may also refer to the fact, that we do not parametrize the structure (which is not always the same as parametrizing the distribution) of our...

p = 1/360 is the probability of success. Look at wikipedia article on geometric distribution: it says "geometric distribution [...] is the probability distribution of the number X of Bernoulli trials needed to get one success". Bernoulli trial means a trial which can have only two outcomes: 1 or...

I assume you understand, that you cannot actually get neither lognormal nor normal distribution, as they are continuous, and your r.v. is discrete. If I understood your description, then your r.v. is just "the number of failures, before first success", where success is getting "EEDCBA" and...

For me a random sequence is clearly a mathematical object. It is a concept. We define a probability space, and also a mapping that maps values of my abstract sample space to sequences. Given a probability measure, I can work with this sequency (mapping) according to certain rules, proving...

Since this is a mathematics forum: A process can still be random even if current/past knowledge does give some help in predicting the outcome (think of markov chains of order > 1). Actually, if the initial state is random, but future changes are fully deterministic given most current state, the...

I might be wrong about this, but I believe mathematics, science (and especially QM...) have nothing to say about this, because it is a philosophical question. I believe it is De Finetti's book (Theory of Probability) that starts with "probability does not exist". Maybe you will find some...

Hmm.. you denote by P_{\Omega | x} just some arbitarily chosen probability measure on (\Omega, \Sigma_\Omega), i.e. you have a family of measures parametrized by x \in \Theta. Then you define To answer the question, whether {P_{\Omega |x}} = \frac{{d{P_{\Theta \times \Omega }}}}{{d{P_\Theta...

I was just quoting your definition of P_{\Theta\times\Omega}. Later in you question you refer to \frac{dP_{\Theta\times\Omega}}{dP_\Omega} as a Radon-Nikodym derivative, but this, as I tried to point out in my previous reply, doesn't make sense.

Perhaps I've misunderstood you, but... f would be a Radon-Nikodym derivative if P_{\Theta\times\Omega}(A) = \int_A f \, dP_\Theta for all A \in \Sigma_\Theta\times\Sigma_\Omega (product sigma-field). However this doesn't make any sense, because you have different measurable spaces on the...