well, the actual problem is show that this function is a pdf. so i need to show that it integrates to 1, which it does, but i believe i also need to show that it's bounded by 0 and 1 for all x in the domain, which is the problem i'm having a hard time with.
Homework Statement [itex]
$f(x)=\begin{cases}
7(4)^{-i} & x\in(\frac{1}{2^{i}},\frac{1}{2^{i-1}}],i=1,2,3,...\\
0 & 0\geq x,x>1
\end{cases}$ (please excuse the poor latex)
Homework Equations
The Attempt at a Solution
the problem i'm having is say x=3/4. then according to the pdf...
Homework Statement
http://i.imgur.com/tjpka.png (the actual problem is the third part down)
Homework Equations
the first two parts are the definition of borel sets,and the second part is a relevant theorem.
The Attempt at a Solution
so I'm new to Borel sets. And I feel like I'm...
alright, sorry i was a bit lazy on the latex, i didn't think it would be that bad originally, and i haven't used latex in a while.
i've attached a pdf. how does that look?
Homework Statement
this is probably a dumb question, but i'm doing this proof where i have to show two sets are equal, where each set is a union from 1 to n sets. this is pretty easy to show with induction, i think, but i'm used to using induction when i have an infinite amount of things, so...
monotonic refers to how it increases. monotonic increasing means each term is greater than or equal to the term before it. monotonic decreasing means each term is less than or equal to the term before it. if it just says monotonic, either situation will work.
the prior probability represents the number of red balls in the urn. i'm told to assume that each possibility is equally likely. so there might be zero balls, 1 ball, 2 balls, etc, up to 9 balls. that should be a 1/10 probability for each case. furthermore, shouldn't the prior column sum up to...
Homework Statement
so i'm trying to teach myself bayes, and i got a book, and i'm going through trying to do the exercises, and lo and behold, i get stuck on the first one. i thought i was getting it, but the answer given at the back of the book is different than mine.
Homework...
also, memorization is important because it allows you to focus on the more important things. after a while it just becomes second nature. it would be hard to do a lot of math if you didn't have certain things memorized, like properties of various operations. you could do it, it would just...
i'm an undergrad in stats, and next semester is my last. i'm doing an independent study next semester, and am unsure of what would be more beneficial for me: a class in R, or bayes. i would like to do bayes, and i'm decent on computers with limited programming experience, so i'm not too worried...
Homework Statement
(excuse lack of latex)
show that if SUM(zn)= S and SUM(wn= T, then SUM(zn + wn) = S + T
Homework Equations
The Attempt at a Solution
so if i'm doing this right, this is pretty easy, i think. they want me to use a theorem that says if zn=xn +iyn, and SUM(zn)= S, where S...