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Dec
2
comment Show $\lim_{n \to \infty} n^{-1} E \left( \frac{1}{X}1_{[X>n^{-1}]} \right) =0$
Suspect the key here is that P[X<∞]=1
Oct
8
comment $P(X_n < a$ i.o. and $X_n > b$ i.o.$) = 0$ for all $a < b$ implies that $lim_{n \rightarrow \infty} X_n$ exists a.e.
Now I'm happy! Thanks!
Oct
8
comment $P(X_n < a$ i.o. and $X_n > b$ i.o.$) = 0$ for all $a < b$ implies that $lim_{n \rightarrow \infty} X_n$ exists a.e.
Should it be x_n_1<a?
Oct
8
comment $P(X_n < a$ i.o. and $X_n > b$ i.o.$) = 0$ for all $a < b$ implies that $lim_{n \rightarrow \infty} X_n$ exists a.e.
Not sure if I understand what you are saying here. Let x_n=7 for all n. So lim x_n=7. But there exists an 'a' in Q such that a<x_n for infinitely many n. For example, a=2. So by your statement lim x_n does not exist.
Sep
24
comment Proof of $\sigma^2\geq (\mu-m)^2$ without resorting to Jensen's or Chebychev's inequality.
Can you pls explain why is P[X<=m]>=1/2?
Sep
9
comment How do I differentiate polynomials
If you dont like your text,try another one. Or en.wikipedia.org/wiki/Calculus#Differential_calculus to get started.
Sep
3
comment Suggested book for self study.
I really like the 4 volume series by Stein & Shakarchi. Fourier stuff, Complex Analysis, Measure theory, Functional analysis. But, your background will determine if they are suitable for self-study.
Aug
14
comment Basic probability limit problem
Since the mean=0, it exists, and is the integral of xg(x) over R. Now assume the limit doesnt hold...could the integral still be zero?
May
28
comment Are upper division math courses textbook- or lecture-based?
I view the teacher as a very experienced tour guide. They point out the interesting parts, explain the difficult parts, show what is important. But it is (always) up to you to do the work.
May
26
comment Show Wright-Fisher Model is a martingale
Been there, done that. Glad it helped.
May
26
comment Show Wright-Fisher Model is a martingale
wouldn't that just be a binomial distribution? and what is the mean of a binomial distribution? (Note I am asking - i could be wrong)
Jan
17
comment What are some good books about martingales?
Williams: Probability with Martingales
Feb
13
comment Can the matrices $A$ and $I+A$ have the same determinant?
do you know about eigenvalues & trace?
Jan
23
comment Division of two random variables of uniform distributions
Just to try out Mathematica's probability framework: D[Probability[ x/y <= z, {x [Distributed] UniformDistribution[{0, 1}], y [Distributed] UniformDistribution[{1, 3}]}], z] yields (for the pdf) 2 if z<1/3, (6-2z)/(4z)-(-z^2+6z-1)/(4z^2) if 1/3<z<1 and 0 elsewhere.
Jan
16
comment Fun but serious mathematics books to gift advanced undergraduates.
+1 for "Proofs and Confirmations" by David Bressoud. It is ridiculously good.
Nov
29
comment Example of two dependent random variables that satisfy $E[f(X)f(Y)]=Ef(X)Ef(Y)$ for every $f$
@NateEldredge: that is what I figured. So if you do the arithmetic, it does not work out. f(1)P(X=1)+f(2)P(X=2)+f(3)P(X=3)=(5x+9y+12z)/30, not (3x+3y+4z)/10....unless I'm seriously caffeine deficient right now.
Nov
29
comment Example of two dependent random variables that satisfy $E[f(X)f(Y)]=Ef(X)Ef(Y)$ for every $f$
Can you pls explain how you got E(f(X))?
Jul
17
comment What does the variance/SD of a set signify?
See the chebyshev inequality.
May
17
comment What's the sum of $\sum_{k=1}^{\infty} e^{-k(x-k)^{2}}$?
Look up the Euler Maclaurin formula....Mathematica can do the integral, and it involves the erf function.
Mar
9
comment Asymptotic behavior of $\sum_{k=1}^{n}\left(1-p^{k}\right)^{n-k}$
@RobertIsrael: Phew - now I can drink the coffee slowly, rather than chugging it. That helps a huge amount, much appreciated!