nomen

I mean, the notation is getting "ugly", but yes it's valid. You can definitely fix points in the domain, condition on them, and take the expectation of the pdf you got by conditioning. In fact, you might want to pick an "easy" continuous distribution and see what you get if you take E(f(X)) (excluding all the conditioning stuff, which is only relevant as a process -- once you "un-condition" a conditional density (by "assuming" the condition), you have a "regular" density).

@nbro: I don't see the problem. The expected value operator is just an integral restricted to the sample space. The reality is that every real function from the sample space is a random variable. (Heck, there are "generalized" random variables, like random matrices, which are reified by mappings from the sample space to the space of matrices)

@Uueerdo: Canadian TV has "Continuum", which also has a "lot" (maybe a dozen characters) of people with time machines fighting a war in their own past. It was a good show.

He said he went and did it with management approval, since he is on downtime.

If you're still working on this, look up 18.3.1 at stat.rutgers.edu/home/hcrane/Teaching/582/lectures/…, which explains (well) what I was getting at (poorly).

You basically want to do an exact version of en.wikipedia.org/wiki/Simple_linear_regression (which is the statistical "sample" based argument)

By the way, I was slightly wrong -- Y isn't necessarily normal, BUT X and Y fit the axioms for the standard linear model, so the correlation is a...

I think the integral would be hard.

Because Y is a linear function of X, so Y is normal.

That depends. In this situation, (X,Y) are jointly normal, so there is a simple formula for the correlation and covariance. But if your book didn't cover it, you'll have to prove the formula.

do you have any formulas to calculate the covariance between X and Y? If so, look at the formula that defines C(X,Y) carefully and see what you can figure out based on the problem data.

Y is a linear function of X, so it is very much not independent. But there are formulas for this situation. (Not that I remember them at the moment, but perhaps they're in whatever book you're using).

Of course there is such a thing as "evidence of something not happening". It's "evidence that something else happened".

The epistemological foundations of mathematics are extremely murky, with the same approximate complexity and difficulty as "big" metaphysical topics as realism versus nominalism versus constructivism.

How is wealth "consumed", and how is that bad for society? 5 is an impossibility, and just bad rhetoric.

so, that sounds good. thanks

we're all volunteers here, i gotcha :)

A lot of what I write about might be too focused on insurance for this blog. But maybe I can expand poissonlabs.com/blog/linearity-of-expectation into an article for next week.

and yes, the other blog is mine :)

i'm not sure. i write for that other blog first, and i think that if i think of appropriate topics for here, i'd be happy to expand and post

@mixedmath: i have a lot of experience with latex. :)

@mixedmath: just making sure you know, but I posted my draft for review.

I'm actually pretty used to Markdown + Mathjax. I just didn't know about $latex ...$

@AlexJBest: okay, thanks, I'll give that a try

Anyway, article submitted for review.

It doesn't seem like $x^2$ works. $$f(x) = ...$$ works fine for displaymode.

How does inline math mode word? dollar-foo-dollar doesn't seem to mathmode my foo's.

@mixedmath: Will Jagy, Binary Quadratic Forms

@mixedmath: yeah, what's up?

@mixedmath: super, thank you.

@mixedmath: okay, sounds good. I've signed in over there.

@mixedmath: I don't have anything ready yet, but I should be done in a couple of hours. After that, how does the submission process work? Where do I post or send it to?

Hello, I'm interested in writing an article on introductory actuarial science, aimed at an undergraduate audience. The goal of the article is to show how why insurance companies are better equipped to handle risk efficiently, and what it means for the risk that you and I, as customers, face. To that end, I would present a problem and work a problem on risk management.