Recent content by Polymath89

I have two basic questions about combinations. If there are e.g. 10 objects of which 3 are identical and you want to pick a group of 6 out of those 10, how many groups could you get in this case? I know how basic combinations work, but what if there are identical objects involved? And my...

I'm currently reviewing pre-calculus material and encountered a little problem with an absolute value expression. |3-x|=x-3 Now the way I learned absolute value expressions was that there's a positive and a negative case. So I got: 3-x=x-3 x=3 and -(3-x)=x-3 gives 0=0. Stupid question...

Ah ok thanks a lot. I thought "not necessarily behind him" meant that he is not allowed to stand behind him (not a native speaker).

Question: Six mobsters have arrived at the theater for the premiere of the film “Goodbuddies.” One of the mobsters, Frankie, is an informer, and he's afraid that another member of his crew, Joey, is on to him. Frankie, wanting to keep Joey in his sights, insists upon standing behind Joey in...

I have a related question to this one. Do you guys think it makes sense to solve problems to which no solutions are given?

Thank you very much.

Sorry for not being clear, yes I want to expand the sum.

I need to simplify this expression and I don't know how to deal with the factorials in the sum e^{-(\lambda + \mu)}\sum_{k=0}^w \frac{\lambda^k \mu^{(w-k)}}{k!(w-k)!} Can anybody give me a hint on how to sum over the factorials?

I think 9!/5!, but wouldn't that ignore the fact that the odd integers can be arranged too?

In how many ways can the digits 1 through 9 be arranged such that [I]In how many ways can the digits 1 through 9 be arranged such that the even digits appear in ascending order? Well I don't really have a good idea on how to solve this. If we start with the scenario: 2 4 6 8 _ _ _ _...

I'm sorry, I just noticed the difference in the terms, first the author uses v as a constant, so he starts with this term: \prod_{i=1}^m[\frac{1}{\sqrt{2\pi v}}\exp{(\frac{-u_{i}^2}{2v})}] and then he gets, by ignoring the constant multiplicative factors: \sum_{i=1}^m...

I have a problem taking the log of this expression \prod_{i=1}^m[\frac{1}{\sqrt{2\pi v}}\exp{(\frac{-u_{i}^2}{2v_{i}})}] Now I would get \ln({\frac{1}{\sqrt{2\pi v}}})(\sum_{i=1}^m{\frac{-u_{i}^2}{v_{i}}}) The author gets, by ignoring the constant multiplicative factors, \sum_{i=1}^m...

I'm reading a finance book in which the author proposes to exclude the mean when calculating the variance of returns, because he thinks it's difficult to distinguish the drift of the price from the variance of that time series. So he basically calculates the sample variance like this...

sorry didn't see that^^ thanks a lot guys.

Im reading Lang's first course in calculus and can't understand one step that he does when trying to integrate quotients with quadratic factors in the denominator. He's trying to find the integral of \int{\frac{1}{(x^2+1)^n}dx} but he's first starting with the case where n=1 Then while...