This makes sense. Then it makes me wonder, since you can't assume WLOG that the first component is 1, how do we argue that there are n-1 DOF rather than n?
What about this simpler case: we want to solve for x\in\mathbb{R}^9 and to do so we collect constraints a_i^Tx=b_i. If we can find 9 of...
Hi, if I were you I'd encode all attributes as integers, so that all records can be stored as rows in a matrix of type int. I'll assume that you've done this, and your database is a matrix "db" of size [numusers 4]. I'll let you work out the details of that. First, let me give names to the...
Suppose that for some application it is mathematically convenient to represent certain objects of interest (e.g., lines or conics) as n-dimensional vectors. That such a representation exists let's us conclude that in order to specify such an object, no more than n values are necessary. That is...
I've run into these formulas many times but I've never seen how they were derived.
Say you want to fit a line to some data. Your data is a bunch of (xi,yi) pairs.
Through some kind of magic, the slope m and the y-intercept b are given by these formulas...
Here's the page: http://mathworld.wolfram.com/Hyperplane.html
They say that the set S is a subspace of R^n. Is that true? Doesn't c have to be zero in order for S (the hyperplane) to be a subspace?
This is something that's bothered me for a very long time...
Say you're doing Gaussian elimination on some matrix.
Now suppose during the process, some row gets zeroed out, say row j. Now it makes perfect sense for me to say that row j was a linear combination of the previous rows.
But...
Ok I see. I forgot that E[...] is kind of like the average of many repetitions. I see what you guys are saying, it makes sense that the average of a bunch of positive numbers is positive. Thanks :)
Ok I know that Var[X] = E[(X-E[X])^2]. But I just can't help but think that the variance should always be zero. I think it makes so much sense, but obviously the formula says otherwise... But look, my reasoning seems so perfect:
1) The variance is the expected difference from the mean...
This is driving me completely crazy!
QUESTION 1: There are two interpretations I find for the exponential distribution:
1) It models the lifetime of something that does not age in the sense that the probability of functioning yet another time unit does not depend on its current age. So...
Thanks for the replies everyone, but I'm still kind of confused as usual... Forget my first post and tell me what you think of this:
Which sentence in that reasoning is wrong?
If there was only one pair of each (2 light, 2 dark) and the first two were the two lights then the is no third light sock so the probability would be 0..? Hmm I don't really see what you're getting at, sorry...
How is this probability reasoning wrong??
Homework Statement
Homework Equations
The professor didn't say it explicitly, but I'm pretty sure that sock choices are taken to be independent, so P(A,B,C) = P(A)P(B)P(C).
The Attempt at a Solution
The last part is easy...the correct...
I'm not a math or physics guru like these guys so I can't really speak from experience, but I've run into some articles on the Web talking about all the linear algebra that Google uses that I think you might like. Here they are:
How Google Finds Your Needle in the Web's Haystack
The...
This is a great book. It isn't filled with tons and tons of problems (it's not a textbook) but it's still very good. It really cuts through the wordy BS and gets to the heart of things.
Remember that if you really can't afford too many books you could very likely find this one at a library...