ࡱ> IKH "bjbj 0>__"$)n$6V(.o"cc">0nB BBDnB : WeekChapterTopics 1 6  JOINTLY DISTRIBUTED RANDOM VARIABLES: Joint PMFs, PDFs, joint continuity, marginal distributions, examples, multinomial distributions 2 6 (cont.) INDEPENDENT RANDOM VARIABLES: Examples, Poisson together with binomial is Poisson with different mean, symmetry characterization of normal distributions, characterization of independence in terms of separation of variables, half-lives.  3 6 (cont.) SUMS OF INDEPENDENT RANDOM VARIABLES, convolutions, sums of uniform, Gamma, Normal, lognormal rvs, Poisson and binomial, rvs. 4 6 (cont.)  CONDITIONAL DISTRIBUTIONS. Discrete case, Continuous case, Examples: t-distribution, Chi-squared, bivariate normal, distribution of the range of a random sample. joint pdfs of functions of more than one random variable. 5 7  PROPERTIES OF EXPECATION: Expectation of sums, estimators, sample mean vs. expected value, examples: binomial, hypergeometric. MIDTERM. 6 7 (cont.) PROPERTIES OF EXPECTATION (cont.), MOMENTS. Expected numbers of runs, Using indicator functions for counting: unions of events and inclusion/exclusion, maximum-minimums identity, Moments of number of events. 7 7 (cont.) MOMENTS (cont.), VARIANCE, COVARIANCE, CORRELATION: Examples of moment calculations: binomial, hypergeometric, negative hypergeometric, Variance, Covariance: independent RVs, variance and covariance of sums. 8 7 (cont.) CONDITIONAL EXPECTATIONS: Conditional expectations as a method for computing probabilities, examples: geometric distribution, conditional variance and covariance, prediction using conditional expectations. 9 7 - 8 MOMENT GENERATING FUNCTIONS, MULTIVARIATE GAUSSIANS, LIMIT THEOREMS: Computations of moment generating functions, descriptions of multivariate Gaussians using covariance matrices, correlations, Matlab visualizations. Markov and Chebyshev inequalities. 10 8 (cont.) LIMIT THEOREMS: Weak and strong laws of large numbers, Central Limit theorem, Other inequalities.MATH 130B Suggested Syllabus Textbook: A First Course in Probability, by S. Ross   1 2 3 4 5 7 8 9 B 蓓p蓓p#h7sh5CJOJQJ^JaJ h7shCJOJQJ^JaJ h0whVWCJOJQJ^JaJh7shVWCJaJ#hVWh5CJOJQJ^JaJ hVWhVWCJOJQJ^JaJhVWCJOJQJ^JaJhVWCJaJh7shCJaJh7sh5CJaJ* /kd$$IflF>&`Jn t 6A 0'    44 lapyt7s$A &#$/Ifgd7s$$A &#$/Ifa$gd7s, & 0` P@$A &#$/1$7$8$H$Ifgd7s$$A &#$/Ifa$gd7sVAAAA$$A &#$/Ifa$gd7skd$$IflF>&`Jn t 6A 0'    44 lapyt7s , & 0` P@$A &#$/1$7$8$H$Ifgd7s$A &#$/Ifgd7s VAAAA$$A &#$/Ifa$gd7skd$$IflF>&`Jn t 6A 0'    44 lapyt7s 3 , & 0` P@$A &#$/1$7$8$H$Ifgd7s$A &#$/Ifgd7s3 4 5 7 8 B C D VAAAAAA$$A &#$/Ifa$gd7skdU$$IflF>&`Jn t 6A 0'    44 lapyt7sB C D E ! " # $ & ' ( ) * + C E ˽ˉ˽{ˉmehjCJaJhjCJOJQJ^JaJh_CJOJQJ^JaJhVW5CJOJQJ^JaJhVWCJaJh7shCJaJ#h7sh5CJOJQJ^JaJhVWCJOJQJ^JaJ h0whVWCJOJQJ^JaJ h7shCJOJQJ^JaJh7shVWCJaJhCJaJ%D E " # )kd$$IflF>&`Jn t 6A 0'    44 lapyt7s, & 0` P@$A &#$/1$7$8$H$Ifgd7s# $ & ' ) * + , & 0` P@$A &#$/1$7$8$H$Ifgd7s$A &#$/Ifgd7s$$A &#$/Ifa$gd7s VAAAA$$A &#$/Ifa$gd7skd$$IflF>&`Jn t 6A 0'    44 lapyt7s )kd$$IflF>&`Jn t 6A 0'    44 lapyt7s, & 0` P@$A &#$/1$7$8$H$Ifgd7s u , & 0` P@$A &#$/1$7$8$H$Ifgdj$$A &#$/Ifa$gdj n t u v w y z | ERSTUWX]^_|LZ[\]`abkl˽ˮ˽ˮ˽˝ˮ˽h_hjCJaJ#h7shj5CJOJQJ^JaJ hjhjCJOJQJ^JaJhj5CJOJQJ^JaJhjCJOJQJ^JaJ h0whjCJOJQJ^JaJ h7shjCJOJQJ^JaJhjCJaJh7shjCJaJ1u v w y z VAAAA$$A &#$/Ifa$gdjkdq$$IflF>&`Jn t 6A 0'    44 lapyt7s ST)kd8$$IflF>&`Jn t 6A 0'    44 lapyt7s, & 0` P@$A &#$/1$7$8$H$IfgdjTUWX^_[, & 0` P@$A &#$/1$7$8$H$Ifgdj$A &#$/Ifgdj$$A &#$/Ifa$gdj[\]`akVAAAA$$A &#$/Ifa$gdjkd$$IflF>&`Jn t 6A 0'    44 lapyt7skl, & 0` P@$A &#$/1$7$8$H$Ifgdj$A &#$/Ifgdjl!"óãuhJh OJQJ^JaJhJhJ6OJQJ^JaJhJhJOJQJ^JaJhJhJ5OJQJ^JaJhVWhVW5OJQJ^JaJ*hVWhJ5OJQJ^JaJ*h7shjCJaJ h_hjCJOJQJ^JaJ h_h_CJOJQJ^JaJ "V44"$ & 0` P@1$7$8$H$a$gdJkd$$IflF>&`Jn t 6A 0'    44 lapyt7s.:p / =!"#$% $$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s$$If!vh#v`#vJ#vn:V l t 6A 0'5`5J5npyt7s"y666666666vvvvvvvvv666666>6666666666666666666666666666666666666666666666666hH6666666666666666666666666666666666666666666666666666666666666666666866666662 0@P`p2( 0@P`p 0@P`p 0@P`p 0@P`p 0@P`p(8HX`~8XV~ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@ 0@666666 OJPJQJ_HmH nHsH tH@`@ NormalCJ_HaJmH sH tH DA D Default Paragraph FontRi@R 0 Table Normal4 l4a (k ( 0No List jj  Table Grid7:V0PK![Content_Types].xmlN0EH-J@%ǎǢ|ș$زULTB l,3;rØJB+$G]7O٭VGRU1a$N% ʣꂣKЛjVkUDRKQj/dR*SxMPsʧJ5$4vq^WCʽ D{>̳`3REB=꽻Ut Qy@֐\.X7<:+& 0h @>nƭBVqu ѡ{5kP?O&Cנ Aw0kPo۵(h[5($=CVs]mY2zw`nKDC]j%KXK 'P@$I=Y%C%gx'$!V(ekڤք'Qt!x7xbJ7 o߼W_y|nʒ;Fido/_1z/L?>o_;9:33`=—S,FĔ觑@)R8elmEv|!ո/,Ә%qh|'1:`ij.̳u'k CZ^WcK0'E8S߱sˮdΙ`K}A"NșM1I/AeހQתGF@A~eh-QR9C 5 ~d"9 0exp<^!͸~J7䒜t L䈝c\)Ic8E&]Sf~@Aw?'r3Ȱ&2@7k}̬naWJ}N1XGVh`L%Z`=`VKb*X=z%"sI<&n| .qc:?7/N<Z*`]u-]e|aѸ¾|mH{m3CԚ .ÕnAr)[;-ݑ$$`:Ʊ>NVl%kv:Ns _OuCX=mO4m's߸d|0n;pt2e}:zOrgI( 'B='8\L`"Ǚ 4F+8JI$rՑVLvVxNN";fVYx-,JfV<+k>hP!aLfh:HHX WQXt,:JU{,Z BpB)sֻڙӇiE4(=U\.O. +x"aMB[F7x"ytѫиK-zz>F>75eo5C9Z%c7ܼ%6M2ˊ 9B" N "1(IzZ~>Yr]H+9pd\4n(Kg\V$=]B,lוDA=eX)Ly5ot e㈮bW3gp : j$/g*QjZTa!e9#i5*j5ö fE`514g{7vnO(^ ,j~V9;kvv"adV݊oTAn7jah+y^@ARhW.GMuO "/e5[s󿬅`Z'WfPt~f}kA'0z|>ܙ|Uw{@՘tAm'`4T֠2j ۣhvWwA9 ZNU+Awvhv36V`^PK! ѐ'theme/theme/_rels/themeManager.xml.relsM 0wooӺ&݈Э5 6?$Q ,.aic21h:qm@RN;d`o7gK(M&$R(.1r'JЊT8V"AȻHu}|$b{P8g/]QAsم(#L[PK-![Content_Types].xmlPK-!֧6 0_rels/.relsPK-!kytheme/theme/themeManager.xmlPK-!g theme/theme/theme1.xmlPK-! ѐ' theme/theme/_rels/themeManager.xml.relsPK] ">B l"  3 D # u T[k" -1!'$$335D$*wU^8k$  p VW7sX _Jjw  "$@!!aa!!"@Unknown G.[x Times New Roman5^Symbol3. *Cx Arial;[xPHelvetica7@CambriaG=  jMS Mincho-3 fgW,|8DengXian LightI{~ LightC.,*{$ Calibri Light? |8DengXianI{~7.* CalibriA$BCambria Math q'h'g-y66!hh20K#QHP $P'2! xxt  Alessandra Pantano_R F Oh+'0|  8 D P\dltAlessandra Pantano Normal.dotm 志勤 陆5Microsoft Office Word@@&@Ic6 ՜.+,0 hp  '$University of California, Irvine  Title !"#$%&')*+,-./012345679:;<=>?ABCDEFGJRoot Entry F3#ccLData  1Table(BWordDocument0>SummaryInformation(8DocumentSummaryInformation8@CompObjr  F Microsoft Word 97-2003 Document MSWordDocWord.Document.89q