Hi all
I am struggling to see the difference between Convergence in probability and Almost surely convergence of a sequence of random variables.
From what i can see Almost surely convergence of Sequence of Random variables is very similar to pointwise convegence from Real analysis.
I am...
Hi
context: i am trying to understand convergence of sequence of random variables.
random variable are just measurable functions but
I still can't get my head around the connection between sequence of functions and sequence of sets. To start suppose A_n \subset \Omega i don't even...
thanks all for you replies, i understand the idea, but still not sure how Average turns out to be 6.i think i am getting it. i need to think it over see what i come up with
thanks i understand that suppose the Probabilty of head is 0.5. apparently the answer is 6 secons but how does
0*P(0) + 1*P(1) + 2*P(2) + ... + n*P(n) + ... = 6 ? that's what i don't understand yet
this is not a homework question, it was a interview question
Question:
suppose we keep flipping an unbiased coin every second, how long do you have to wait on average before you get two heads in a row.
similar question here http://www.wilmott.com/messageview.cfm?catid=26&threadid=16483...
Hi this is more of a set theory question really, I'm a bit confused,
say \mathcal{F} is collections of sets, and \mathcal{F}_n is a sequence of sub collections of sets and say B_{1}, B_{2} ... is a sequence of sets
what does the following mean \mathcal{S} = \{ A \in \mathcal{F}...
i think i may have figured it out. i graphed the function f(x) and realized it was symmetrical, f(x) = f(1-x) \, x \in [0,1] i then realized to find to generated sigma-field \sigma(f(x)) = \{ f^{-1}(B) \colon B \in \mathcal{B} \} the inverse image for any borel set is the union of two...
suppose we have a X = [0,1] and a function f\colon X \to \Re where
f(x) = 1 - |2x -1| .
i'm bit confused on finding the sigma-algebra generated by this function. This is what i did
f(x)= \begin{cases}
2 -2x & x \in [\frac{1}{2},1] , \\
2x& x \in...
thanks for you reply, so absoulte continuity guarantee's the functions has a derivative then ?
if so why, are there any good resources or books, where this is proved/explained in more detailed
hey i had to re-learn calculus too! it has been over almost 10 years since my undergrad degree. what i did was i worked throught some of the exercises provided by mit open course ware http://ocw.mit.edu/OcwWeb/Mathematics/18-01Fall-2006/Readings/detail/course-reader-.htm
I also bought this...
i'm going through a proof and i can't seem to workout why this equality makes sense
\sum^{10^{i}-1}_{k=0} \frac{k}{10^i} = \frac{(10^i-1)}{2}
this may be obvious, any hints atleast would be much appreciated
i'm having a difficult time trying to grasp what absolute continuity means, i understand uniform continuity. i can't seem to distinguish between the them.
to me it seems that if f on some inteval [a,b] is uniformly continuous then it would be absolutely continuous ?
is there a visual way...
okay here is my second attempt:
A measure is a set function \mathcal{F} \to \Re . where \mathcal{F} is a sigma-algebra. the invariants it must satisfy are it countable additive and the measure of a null-set is zero.
Now integral \int_{B} f d\mu is nothing but a special case of a measure...
suppose we have random variable defined a function of another random variable such that Y = \mathbb{E}(X)
it seem then Y is a constant. then \mathbb{E}(Y) = \mathbb{E}(X) does this even make sense ?