Eric

economics, #rstats,

[Eric @expersso]

Fun question to solve with #mathematica.

[Quantіan @quantian1]

Junior data scientist interview question: Assume you generate points X = N(0,1); Y = N(0,0.1). Rotate the (x,y) dataset 45 degrees, so they look something like pic below (line is y = x). If you were to calculate the OLS regression y = b1*x + b0, what is E[b1] as n->infinity?

[Eric @expersso]

@GWOMaths Or using recursion:

roll <- function(total = 0) {
if(total > 25) total else roll(total + sample(6, 1))
}

table(replicate(150, roll()))

[Eric @expersso]

@RyanDavidReece @KyleCranmer Chi2(n) is just Gamma(n/2,1/2), so maybe that’s what you’re looking for.

[Eric @expersso]

@joe_shipman It's given here (albeit without citation): https://t.co/O6435V6XOz

[Eric @expersso]

@nntaleb @CutTheKnotMath And so T[xs, {-1,0,0}] gives the (inverse) harmonic mean and T[xs, {2,0,0}] / T[xs, {1,0,0}] gives the contraharmonic mean. Neat!

[Eric @expersso]

@FiveThirtyEight 3/8 (by exhaustive enumeration)

[Eric @expersso]

My solution using #Mathematica @WolframResearch .

[Eric @expersso]

@nntaleb @DrCirillo For those needing the proof spelled out in a bit more detail:

[Eric @expersso]

@calvinmdewilde Yeah, I got a rude email from a CRAN maintainer saying that the package produced an error whenever the WHO website was down, so they just archived it. You can still get it on github though: https://t.co/eFddRWTmlX

[Eric @expersso]

@michael_chirico dtpois <- function(lambda,xmin,xmax) {
p<-dpois(xmin:xmax, lambda)
p/sum(p)
}
sample_wo_rep<-function(n,dist,y=NULL) {
if(n<=0) return(y)
x<-sample(seq_along(dist),1,prob=dist)
dist[x]<-0
sample_wo_rep(n-1,dist/sum(dist),c(y,x))
}
sample_wo_rep(8,dtpois(5,1,12)) ?

[Eric @expersso]

@michael_chirico Yeah, I see what you're trying to do. It's an interesting problem. Perhaps one could look at it as a hierarchical model with X ~ MultivariateHyperGeometric(N=12, K=(1,1,...,1),n=Y) with Y ~ TruncatedPoisson(5, trunc = (1,12)) and then somehow allow for biased urn sampling.

[Eric @expersso]

Fun way to solve this problem in #Mathematica using built-in optical character recognition and translation.

[Your Daily Epsilon of Math @Daily_Epsilon]

Today's #dailymaths problem from the Mathematics 2020 calendar in pic. Solution will post tomorrow. Daily problems with previous day's solution are tweeted ~6am Eastern. Solutions by me and/or @MathsTim unless otherwise stated. Guest solution posts welcome--DM if interested.

[Eric @expersso]

Cobweb plots in #Mathematica.

[Analysis Fact @AnalysisFact]

New post: Cobweb plots
https://t.co/rvmesHAmFh

[Eric @expersso]

@ChelseaParlett @goldblatchikens @Billistician 7. Arises naturally as the order distribution of uniforms. 💯

[Rush @rushtheband]

Neil Peart September 12, 1952 - January 7, 2020

[Eric @expersso]

Simple optimization problem today:
#Mathematica #WolfLang

[Your Daily Epsilon of Math @Daily_Epsilon]

Today's #dailymaths problem from the Mathematics 2020 calendar in pic. Solution will post tomorrow. Daily problems with previous day's solution are tweeted ~6am Eastern.

[Eric @expersso]

My solutions in #Mathematica #WolfLang and #rstats.

[Your Daily Epsilon of Math @Daily_Epsilon]

Today's #dailymaths problem from the Mathematics 2020 calendar in pic. Solution will post tomorrow. Daily problems with previous day's solution are tweeted ~6am Eastern. Today’s is perhaps trickier than it seems, so good luck!

[Eric @expersso]

@rlmcelreath I'm expecting a lot of "Stop trying to make 'trank' happen, Richard. It's never gonna happen!" in response to this.