probability and statistical inference - nitis mukhopadhyay

... considering my book and wish you all the very best. Nitis Mukhopadhyay January 1, 2000 Preface This textbook aims to foster the theory of both probability and statistical inference for first-year graduate ... simple examples and exercises then drive the point home. One will discover out- of-the-ordinary remarks, ideas and examples throughout the book. e) The history of stati...

Ngày tải lên: 31/03/2014, 16:25

... a se- quence of independent and identical experiments in which we observe whether 120 CHAPTER 6. SUMS AND AVERAGES OF RANDOM VARIABLES or not A occurs. Let p = P (A) and define independent and ... VARIABLES y f(y) -4 -2 0 2 4 0.0 0.1 0.2 0.3 0.4 Figure 4.9: Probability Density Functions of T ∼ t(ν) for ν = 5, 30 F Distributions Finally, let Y 1 ∼ χ 2 (ν 1 ) and Y 2 ∼ χ 2 (ν 2...

Ngày tải lên: 16/01/2014, 16:33

... .0010 -3 .0 .0013 -2 .9 .0019 -2 .8 .0026 -2 .7 .0035 -2 .6 .0047 -2 .5 .0062 -2 .4 .0082 -2 .3 .0107 -2 .2 .0139 -2 .1 .0179 -2 .0 .0228 -1 .9 .0287 -1 .8 .0359 -1 .7 .0446 -1 .6 .0548 -1 .5 .0668 ... .0548 -1 .5 .0668 -1 .4 .0808 -1 .3 .0968 -1 .2 .1151 -1 .1 .1357 -1 .0 .1587 -0 .9 .1841 -0 .8...

Ngày tải lên: 13/09/2012, 09:49

... anti-parallel to the field. We therefore have a system of N spins, each of which can exist in either a spin-up or spin-down state. The energies associated with the spin-up and spin-down ... pressure and temperature at the end of it doing some work then there is no temperature change, i.e. • Initial temperature and pressure = T 0 and P 0 • Final temperature and pressu...

Ngày tải lên: 20/12/2013, 19:15

... also be use- ful for those with reading-related learning disabili- 523 ties and adult literacy students. In both of these sit- uations, as in the bilingual education case, the stu- dent’s reading ... uses n- gram language models as a low-cost automatic ap- proximation of both syntactic and semantic analy- sis. Statistical language models (LMs) are used suc- cessfully in this way in othe...

Ngày tải lên: 20/02/2014, 15:20

... Character Shape Similarity and Statistical Language Model Masaaki NAGATA NTT Information and Communication Systems Laboratories 1-1 Hikari-no-oka Yokosuka-Shi Kanagawa, 23 9-0 847 Japan nagata@nttnly, ... quality photocopies, and faxes are still difficult to process and cause many errors. The accu- racy of handwritten OCR is still about 90% (Hilde- brandt and Liu, 199...

Ngày tải lên: 20/02/2014, 18:20

... Unseen-prob-mass(cmp-form) = number-of-applicable-schemata(cmp-form) I ~eq( cmp-form ) + number-of-applicable-schemata( cmp-form ) Prod(csl) Estimated-freq(interpretationi with cmp-formj) = Unseen-prob-mass(cmp-formj) ... general-nn [ possessive /1\ ] made-of] purpose-patient deverbal / I n°n-derived-pp I I deverbal-pp ] linen chest ice-cream container Figure 2: Fragment of hier...

Ngày tải lên: 22/02/2014, 03:20

... Exchangeability and the evolution of large populations. Pages 97–112 of: Koch, G., and Spizzichino, F. (eds), Ex- changeability in Probability and Statistics. Amsterdam: North-Holland. Proceedings ... Ibragimov, I. A., and Linnik, Yu. V. 1971. Independent and Stationary Sequences of Random Variables. Groningen: Wolters-Noordhoff Pub- lishing. With a supplementary chapter by I. A. I...

Ngày tải lên: 05/03/2014, 22:21

... syntactic tree (Yamada and Knight, 2001).) In the noisy-channel framework, a mono- lingual corpus is used to derive a statistical lan- guage model that assigns a probability to a se- quence of words ... translated per- fectly only 4 0-4 2% of them. 1 Introduction Over the last decade, much progress has been made in the fields of example-based (EBMT) and statistical machine translat...

Ngày tải lên: 17/03/2014, 07:20

... known that if the probability density function is standard nor- mal, that is f(x) = 1 √ 2π e − 1 2 x 2 , −∞ < x < ∞, then the mean µ = 0 and the standard deviation σ = 1, and the area between the ... saying the probability that a random variable is within k standard deviations of the mean is at least 1 − k −2 . Theorem 4.4 (Chebychev Inequality). Let X be a random variable with...

Ngày tải lên: 17/03/2014, 14:20