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...
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...
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...
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...
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.