Recent content by pluviosilla

Why is the Maximum Likelihood function a product? Explanations of how the Maximum Likelihood function is constructed usually just mention that events are independent and so the probability of several such events is just the product of the separate probabilities. I get the logic w.r.t...

The slope of a fitted line = Cov(X,Y)/Var(X). I've seen the derivation of this, and it is pretty straightforward, but I am still having trouble getting an intuitive grasp. The formula is extremely suggestive and it is bothering me that I can't quite see its significance. Perhaps, my mental...

Great response! Thanks!

Homework Statement Suppose we want to estimate a sample proportion to within 0.05 with 95% confidence, how large will the sample have to be? There is no other information about the distributions of the population or the sample. How do I approach this problem? Homework Equations See...

Where are you taught that an integral is actually just a linear function of the integrand? Analysis class, perhaps? I somehow managed to get a bachelor's degree in physics without a single course in analysis, chemistry or - alas - statistics. In the interview I had with the department chairman...

I see! You might say the indicator function takes the place of the integration limits. That's powerful! It was your last statement (Integrate PDF * Expression with Indicator Function) that made this click for me. I'm a self-taught statistician, so I've got these annoying gaps in my training...

Yes, of course. This approach should have been obvious, but I didn't think of it. Thanks! Do you understand how to prove the identity using the indicator function?

I read the Wikipedia article which provides the identities you used above. In particular, I_{A \cap B} = I_A \cdot I_B Are you saying that we can extrapolate this relationship to all functions of an intersection? If so, how would you prove that? It is true that a CDF is, in a sense, a...

Fascinating! I'll read up on the indicator function, because it looks like something I could use to find shortcuts! :-) A couple of questions (if you have time): (1.) Does the equation you posted require X & Y to be independent RVs? (2.) What do you get when the two parentheses are ORed...

I ran across this identity in some actuarial literature: Pr( (x_1 \le X \le x_2) \ \cap \ (y_1 \le Y \le y_2) ) = F(x_2, y_2) - F(x_1, y_2) - F(x_2, y_1) + F(x_1, y_1) First of all, I am not certain this is correct. I think the expression on the LHS is equal to the following double...

Please disregard my question about the righthand term. I'm used to seeing Bayes THM with an AND term in the numerator, so my left brain took over and I did not *see* the conditional term, which of course, explains why you need the righthand term. APOLOGIES! However, I am also not sure I...

Thanks for this reply! How about the right hand term? I refer to this: \frac{Pr(x < X < x + dx)}{dx} This term gives the non-conditional marginal PDF f(x), and the point of the identity seems to be to show that you can represent a conditional PDF as a product of a non-conditional PDF...

I ran across this identity for a conditional PDF where the dependent random variable X is continuous and the independent variable N is discrete: \frac{P(x<X<x+dx|N=n)}{dx}=\frac{P(N=n|x<X<x+dx)}{P(N=n)}\frac{P(x<X<x+dx)}{dx} In the limit as dx approaches 0 this yields: f_{X|Y}(x|n)...

Picture of a classic slide carousel...

I need to program a rotating slide photo carousel, and it is a bit tricky, because in addition to the rotation of the carousel that holds the "slide" images, you need to correctly rotate the individual slide images. The rotation of the individual slide image is obviously dependent on the...