PeterR
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 Mar23 awarded Revival Mar19 comment Winning in roulette when betting on one number infinitely Probability distribution of what? Jan20 comment Does $\int_0^\infty e^{-x}\sqrt{x}dx$ converge? If in the integral it were x, rather than Sqrt[x], the integral would be the mean of the exponential distribution with parameter 1, which is known to have value 1. You can easily do that with integration by parts. Then, since Sqrt[x]n^{-1}]} \right) =0$Suspect the key here is that P[X<∞]=1 Oct8 comment$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$exists a.e. Now I'm happy! Thanks! Oct8 comment$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$exists a.e. Should it be x_n_1 b$ 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=1/2? Sep15 answered Prove that: if $x \sqcup \bar{y}=1$, then $x \sqcup y=x$ (in a Boolean algebra) Sep9 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. Sep3 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. Aug14 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? May28 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. May26 comment Show Wright-Fisher Model is a martingale Been there, done that. Glad it helped. May26 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) Jan17 comment What are some good books about martingales? Williams: Probability with Martingales Jun7 awarded Necromancer Feb13 comment Can the matrices $A$ and $I+A$ have the same determinant? do you know about eigenvalues & trace? Jan23 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