Recent content by Adeimantus

This is going to take a while to set up, so I apologize for that. This came up in the course of thinking about the Strong Law of Large Numbers. It's not homework. Suppose you have a doubly infinite sequence of random variables X_{i,n} that obey the following almost sure convergence relations...

Excellent points. Also, thank you for suggesting Stein's method. I looked it up on Wikipedia, and that may be exactly what I'm looking for!

I agree that since tables of binomial probabilities are readily available, it makes sense to use them. Especially since they are now accessible with the call of a function in R, for instance. But then I'm left wondering, why does anyone care about the limit theorem? Does it have a use...

Okay, but it will never be exactly the same, right? So even there, don't you need to consider how big the range is where the two distributions will lead to opposite conclusions. And then reason, I suppose, that if this range is small, then the approximation is good enough. In other words, you...

Okay, that makes sense. In cases where you would want to use the approximation, how do you quantify how good the approximation is?

That is a good point. So in that case, how would you decide when the approximation is good enough?

What is the preferred method of measuring how accurate the normal approximation to the binomial distribution is? I know that the rule of thumb is that the expected number of successes and failures should both be >5 for the approximation to be adequate. But what is a useful definition of...

No kidding. Thanks guys, it was fun.

Why would I do that? I've said over and over that it is the same thing as P->Q.

At last. Thank you.

Yes, that is correct. And yes, I read your edit. It is absolutely the case that almost nobody ever actually bothers to dissect the meaning "if and only if". Although I am not a mathematician, I would imagine that many professional mathematicians don't bother about it, because it's not that...

Here's the first sentence of the Wikipedia article on "if and only if". https://en.wikipedia.org/wiki/If_and_only_if

If you use the IF-THEN construction, you change the order of P and Q to distinguish directions. If you use the IF and ONLY-IF constructions, you leave P and Q in the same order. In case this is a point of confusion, "P if Q" is not the same as "if P, then Q". Instead, it's actually the same...

I think we can agree that there are logically correct formulations that sound so awkward and pointless that nobody would bother to say them that way. The majority of logically correct statements are not very informative, and sound kinda ridiculous.

I agree with you. And I didn't say that. I said "if P then Q" is the same as "P only if Q". The "only if" is applying to the Q, not the P.