nhaliday + binomial   10

Lecture 14: When's that meteor arriving
- Meteors as a random process
- Limiting approximations
- Derivation of the Exponential distribution
- Derivation of the Poisson distribution
- A "Poisson process"
nibble  org:junk  org:edu  exposition  lecture-notes  physics  mechanics  space  earth  probability  stats  distribution  stochastic-processes  closure  additive  limits  approximation  tidbits  acm  binomial  multiplicative 
september 2017 by nhaliday
st.statistics - Lower bound for sum of binomial coefficients? - MathOverflow
- basically approximate w/ geometric sum (which scales as final term) and you can get it up to O(1) factor
- not good enough for many applications (want 1+o(1) approx.)
- Stirling can also give bound to constant factor precision w/ more calculation I believe
- tighter bound at Section 7.3 here: http://webbuild.knu.ac.kr/~trj/Combin/matousek-vondrak-prob-ln.pdf
q-n-a  overflow  nibble  math  math.CO  estimate  tidbits  magnitude  concentration-of-measure  stirling  binomial  metabuch  tricki  multi  tightness  pdf  lecture-notes  exposition  probability  probabilistic-method  yoga 
february 2017 by nhaliday
probability - How to prove Bonferroni inequalities? - Mathematics Stack Exchange
- integrated version of inequalities for alternating sums of (N choose j), where r.v. N = # of events occuring
- inequalities for alternating binomial coefficients follow from general property of unimodal (increasing then decreasing) sequences, which can be gotten w/ two cases for increasing and decreasing resp.
- the final alternating zero sum property follows for binomial coefficients from expanding (1 - 1)^N = 0
- The idea of proving inequality by integrating simpler inequality of r.v.s is nice. Proof from CS 150 was more brute force from what I remember.
q-n-a  overflow  math  probability  tcs  probabilistic-method  estimate  proofs  levers  yoga  multi  tidbits  metabuch  monotonicity  calculation  nibble  bonferroni  tricki  binomial  s:null  elegance 
january 2017 by nhaliday
reference request - The coupon collector's earworm - MathOverflow
I have a playlist with, say, N pieces of music. While using the shuffle option (each such piece is played randomly at each step), I realized that, generally speaking, I have to hear quite a lot of times the same piece before the last one appears. It makes me think of the following question:

At the moment the last non already heard piece is played, what is the max, in average, of number of times the same piece has already been played?

A: e log N + o(log N)
q-n-a  overflow  math  math.CO  tidbits  puzzles  probability  magnitude  oly  nibble  concentration-of-measure  binomial 
january 2017 by nhaliday

bundles : math

related tags

acm  additive  additive-combo  advanced  alg-combo  algebra  algebraic-complexity  algorithms  AMT  approximation  atoms  better-explained  binomial  bits  bonferroni  calculation  cheatsheet  classic  closure  communication-complexity  concentration-of-measure  concept  convexity-curvature  course  curvature  data-structures  distribution  earth  elegance  entropy-like  estimate  exposition  fields  fourier  geometry  harvard  hi-order-bits  identity  information-theory  integral  lecture-notes  levers  limits  linear-algebra  list  lower-bounds  madhu-sudan  magnitude  math  math.CA  math.CO  math.CV  math.FA  math.MG  math.NT  math.RT  mechanics  metabuch  mihai  monotonicity  motivation  multi  multiplicative  nibble  oly  org:edu  org:junk  org:mat  overflow  p:*  papers  pdf  physics  polynomials  probabilistic-method  probability  problem-solving  proofs  puzzles  q-n-a  quantifiers-sums  quixotic  rec-math  reference  s:*  s:null  space  space-complexity  stat-mech  stats  stirling  stochastic-processes  sublinear  survey  synthesis  tcs  tensors  tidbits  tightness  topics  tricki  unit  wiki  yoga  👳 

Copy this bookmark: