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 lets 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 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...
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 sort of in a bad dilemma right now and need some advice. I'm a CS major and I've slowly grown to like math more and more and coding and the usual CS stuff less and less. In short, math has become my new passion and I'm thinking of changing my major even though I'm 2.5 years into my CS degree...
This is driving me nuts:
How do you show that that's true?!? How do you prove it? For the life of me I can't see how this holds despite the fact that I've wasted the past two hours working at it. I can't think of a technical explanation for it (a proof) OR an intuitive one... Please help.
My teacher gave us an intuitive idea of what it means for two vectors in \mathbb{R}^2 to be linearly independent (they aren't multiples of each other) and for three vectors in \mathbb{R}^3 (they aren't on the same plane).
Now the book has generalized the idea of linear independence to n...
Telling if three vectors in the same plane?? Help!
Hey guys I've got a question about vectors that's confusing me. Here's what my book says:
I don't understand the example... How do you tell if three vectors in R3 are in the same plane? Why does adding the first two and getting (1,1,1) show...
At my school multivariable calculus (aka calculus 3) isn't required under the computer science corriculum. I'll have to take other math courses but we're not forced to take calculus 3 and as far as I know it is not a prerequisite to any computer science course my school offers. The subject seems...
PLEASE help me understand this paper! (Formal math stuff)
Right now in my class we're being given a short introduction to theoretical CS. We're learning not from a book but from our teacher's Ph.D. thesis! The thesis is HEAVY on formal math and I can't follow it... I've been trying for DAYS and...
Hey guys, I'm having trouble solving this definite integral. I'm doing work with polar equations and I was led to this:
http://img404.imageshack.us/img404/6021/first4hv.gif [Broken]
which I simplified to
http://img404.imageshack.us/img404/669/second8qs.gif [Broken]
And, using the...
Please for the love of god help me.
I have a fundamental misunderstanding of differentials and Leibniz notation. I'm confused as to even where I should begin. Please allow me to start off my explanation by showing how my book introduces u-substition:
I have highlighted in red the parts I am...