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(5) æ+÷ó÷:% ó'åé /'ù æ7÷ó;÷ %Ví0÷8öÕñ¡è øôgùðå 7æ=ö.ù 7æ+÷'øù = ý <> Yøùú]æAè/õñò¡? ö ù æû=÷ ùl@ ì +óDè öùð]óôg.ù è/ùð=åöÕñbæ=ç#í0ó'åé /'ùÕ5ñò¡éGóð=ôGò 8 3 p q ó =åLæ+ð-å 7æ=ö.ù 7æ=é û è Sû=ðDó'çô/ú]æ+ðæ7÷ó÷'ôGùð+ýfþ÷ ùA ð +úDð=ôGçTè öùlôgôGù êì[çùlìÀöç#ñò ÷öùë àáVâ4313B<> Yøùú]æ=çëC/'åL÷'ôGùú]ð • limn→∞. √1 n. • limn→∞. R1. • limn→∞. 0. R1 0. R1 0. ... .... .... R1 0. R1 0. R1p 0. x21 + ...x2n D. n f ( x1 +...+x )dx1 ...dxn D n. f ([x1 ...xn ]1/n ). ý. àáVâ43EGF ùð]ú! ] üDó¦ôgùðDæ+÷øIðDî=ôGçì[ù0æ=ì[ùðYôgôGçì[ù0øH#ñ öçì[ùIå-7æ!

(6) L÷ó+æYùðKû=ð]óô#ñò ÷ ûôGçì +óú=ùlJô 'é ý F Xùð]1ú!, Y1 , X2 , Y2 , ... K. ]ü]ó7æ=ùðML]éPôJúû ì[ùðYåLæ+÷ø£ô/÷#í ýAäN÷7îYíÕî+ð [0, 1]. f : [0, 1] → [0, 1]. Zi = 1{f (Xi )>Yi }. n. lim. n→∞. O0P:QNRS+TU6V WYX RHZ2[]\ S]RHW ^^JT6X!_. Xn. ` a. lim. n→∞. O0P:QNRS+TU6V WYX RHZ2[]\ S]RHW ^^JT6X!_. Xn. ` a. lim. ô/÷. 1X Zn = n i=1. Z. 1. f (x)dx p.n. 0. Wcbd^Rfe]OhgjilknmoWp qHR. Sn − ESn = 0, p.n., Sn = X1 + ...Xn . n Wcbd^RferJgjilknmoWp qHR. n→∞. Sn − ESn = 0, P, Sn = X1 + ...Xn . n. àáVâ436s¸äN÷7îYíî7ð û=ðêøù ø£é. æ=ì[ùðYôgô/ðôgùðñåLð=øö÷'ô/ðt öÕñ¡è'øôGùðu/åL÷ôgùúDæ'ôGçì D 2 Sn 0 Xn n→∞ n2 ó'åé /'ùlì® ì ìðYô4úYùðYí ò Nú=ù. lim / ñ!èGð-

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(8) b÷ó+æ=ùð P(Xn = n + 1) = P(Xn = −n − 1) = pn , P(Xn = 0) = 1 − 2pn. ñ¡èGð

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(11) ôGù÷Sû vVäAwyx5÷ø`ðôgùð ñ¡èGð

(12) SôGù÷ û . ~. MP W L. ý.

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