Primery_reshennyh_zadach (514390)

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G_ihkj_^kl\_ggucih^kqzl\_jhylghkl_cG_aZ\bkbfhklvkh[ulbcL_hj_fukeh`_gbybmfgh`_gby\_jhylghkl_c1.1.GZclb\_jhylghklvpnlh]hqlhkemqZcgh\u[jZggh_gZlmjZevgh_qbkehbafgh`_kl\Z{1, 2,…, n} ^_eblkygZnbdkbjh\Zggh_gZlmjZevgh_qbkehk. GZclb lim pn .n →∞nJ_r_gb_kj_^baZ^Zggh]hgZ[hjZqbk_ebf__lky   djZlguokIhwlhfmihdeZkkbq_k n n 1  n −1kdhfmhij_^_e_gbx\_jhylghklb pn =  k  ⇒ lim pn = ≤ pn ≤.→∞nnk  nknk 1.2. Ba fgh`_kl\Z ^ « n` kemqZcgh \u[bjZ_lky qbkeh a GZclb \_jhylghklv lh]hqlhqbkehag_^_eblkygbgZh^ghbagZlmjZevguobihiZjgh\aZbfghijhkluoqbk_ea1,…,akGZclb lim pn .n →∞nJ_r_gb_gZdZ`^h_baqbk_eai ^_eblky   qbk_ebaZ^Zggh]hgZ[hjZlh]^Zihkdhev ai kndmai ihiZjgh\aZbfghijhklugbgZh^ghbagbog_^_eylky xn = n − ∑   qbk_eIhdeZki =1  ai kbq_kdhfmhij_^_e_gbx\_jhylghklb pn =kxn1; lim pn = 1 − ∑ ZgZeh]bqghn n →∞i =1 ai1.3.

Bafgh`_kl\Z^«n`kemqZcgh\u[bjZ_lkyqbkehaImklvpn – \_jhylghklvlh]hqlha2 – 1 ^_eblkygZGZclb lim pn .n →∞J_r_gb_bkdhfh_kh[ulb_j_Zebam_lky\ljzokemqZyo±Z±djZlghZdjZlghZ±djZlghbZdjZlghIhke_^gbckemqZck\h^blkyd^\mfi_j\ufihkdhevdm_kebh^ghbaqbk_e±qzlgh_lhb^jm]h_hlebqZxs__kygZlZd`_ qzlgh_ Ih1 n − 1  n + 1p;lim.wlhfm pn = +=n5 10   10  n →∞1.4.Badheh^udZjldZjlu\ugbfZxlh^gh\j_f_gghdZjluJZkkfZljb\Zxlkykh[ulby:±kj_^b\ugmluodZjlohly[uh^gZ[m[gh\Zy<±kj_^b\ugmluodZjlohly[uh^gZq_j\hggZyGZclb\_jhylghklvkh[ulby C = A ∪ B.4n44313 1J_r_gb_: p A = pB = 1 −   ; p A∩ B = 1 −   ⇒ pC = p A + pB − p A∩ B = 1 − 2   +   .424 21.5.ImklvΩ = {w1, w2, w3, w4} – ijhkljZgkl\hwe_f_glZjguobkoh^h\b\k_we_f_glZjgu_ bkoh^u jZ\gh\_jhylgu JZkkfZljb\Zxlky ke_^mxsb_ kh[ulby A = {w1, w2}; B = {w1,w3}; C = {w1, w4}.

GZclb\_jhylghklbkh[ulbc:, <bKY\eyxlkyebmdZaZggu_kh[ulbyg_aZ\bkbfufb"A 1J_r_gb_ kh]eZkgh deZkkbq_kdhc ko_f_ jZkqzlZ \_jhylghklb p ( A) == = p (B) =Ω 2= p (C ). Kh[ulby:b<y\eyxlkyg_aZ\bkbfufb_kebp(AB) = p(A)·p(B). AB = BC = AC = :<K= {w1} ⇒ p ( AB ) =1 1 1= ⋅ = p ( BC ) = p ( AC ) = p ( ABC ) , ihwlhfm iZju kh[ulbc :<, :K b4 2 23<Kg_aZ\bkbfuH^gZdhkh[ulby:, <bKaZ\bkbfu\kh\hdmighklbihkdhevdm1 1≠  .4 21.6. Imklv j_amevlZl g_dhlhjh]h kemqZcgh]h wdki_jbf_glZ khklhbl \ ihy\e_gbb ljzof_jgh]h^\hbqgh]h\_dlhjZo1, o2, o3ijbqzf\_jhylghklbj1,...

j8ihy\e_gby\_dlhjh\khhl\_lkl\_gghlZdh\up1 = P {( 0, 0, 0 )} = 0,14;p2 = P {(0, 0,1)} = 0,11;p3 = P {( 0,1, 0 )} = 0,11;p4 = P {(0,1,1)} = 0,14;p5 = P {(1, 0, 0 )} = 0,11;.p6 = P {(1, 0,1)} = 0,14;p7 = P {(1,1, 0 )} = 0,14;p8 = P {(1,1,1)} = 0,11.JZkkfZljb\Zxlkykh[ulby: = {(x1, x2, x3): x1 = 0}, B = {(x1, x2, x3): x2 = 0}, C = {(x1, x2,x3): x3 = 0}.

GZclb\_jhylghklbkh[ulbc:, <bKY\eyxlkyebmdZaZggu_kh[ulbyg_aZ\bkbfufb"J_r_gb_ kh[ulby b y\eyxlky g_i_j_dju\Zxsbfbky qZklyfb kh[ulby : ihwlhfmp(A) = p1 + p2 + p3 + p4 = 0.5; ZgZeh]bqghp(B) = p(C) = 0.5. p(AB) = p1 + p2 = 0.25; ZgZeh]bqghp(AC) = p(BC) = 0.25 = p(A)·p(B). LZdbfh[jZahfkh[ulbyA, B bKihiZjghg_aZ\bkbfubaZ\bkbfu\kh\hdmighklb1.7.;jhkZxlky^\_b]jZevgu_dhklbImklvj±qbkehhqdh\\uiZ\r__gZi_j\hcdhklbk±qbkehhqdh\\uiZ\r__gZ\lhjhcdhklbJZkkfZljb\Zxlkyke_^mxsb_kh[ulby: = {(j,k):k = 1,2,5}; B = {(j,k): k = 4,5,6}, C = {(j,k): j + k =9}. GZclb\_jhylghklbkh[ulbc:, <, K, :<,:K, <K, :<K.A 3⋅ 6 1J_r_gb_ kh]eZkgh deZkkbq_kdhc ko_f_ jZkqzlZ \_jhylghklb p ( A) === =Ω 6⋅6 2= p ( B ) , ]^_Ω±ijhkljZgkl\h\k_o\hafh`guobkoh^h\\ZjbZglh\\uiZ^_gby^\modhk1l_cK = {(4,5); (5,4); (3,6); (6,3)} ⇒ p (C ) = .

AB = {(j,k): k = 5}, AC = {(4,5)}, BC = {(4,5);9111(5,4); (6,3)}, ABC = {(5,4)} ⇒ p ( AB ) = , p ( AC ) = p ( ABC ) = , p ( BC ) = .63612<aZ^ZqZo±lj_[m_lkyhij_^_eblvgZ^z`ghklv\_jhylghklv[_ahldZaghcjZ[hlu\l_q_gb_g_dhlhjh]hnbdkbjh\Zggh]h\j_f_gbL ijb[hjZ ko_fZ dhlhjh]h ijb\_^_gZ \ khhl\_lkl\mxs_c aZ^Zq_ GZ^z`ghklv dZ`^h]h we_f_glZ jZ\gZ j Ijb[hj kqblZ_lky jZ[hlZxsbf _keb g_ ih\j_`^_gghc hklZzlky ohly [u h^gZ p_ihqdZ hl ©\oh^Z d \uoh^mª ko_fuIj_^iheZ]Z_lkyqlhwe_f_glu\uoh^ylbakljhyg_aZ\bkbfh^jm]hl^jm]Z1.8.J_r_gb_ ijb ihke_^h\Zl_evghf kh_^bg_gbb g_h[oh^bfZ h^gh\j_f_ggZy jZ[hlZ \k_owe_f_glh\ lh _klv gZ^z`ghklb i_j_fgh`Zxlky ijb iZjZee_evghf kh_^bg_gbb g_h[oh^bfZjZ[hlZohly[uh^gh]hbawe_f_glh\lh_klvgZ^z`ghklvfh`_l[ulvjZkkqblZgZdZd_^bgbpZfbgmk\_jhylghklv©hldexq_gbyª\k_owe_f_glh\iZjZee_evghcp_ib±qn, ]^_q = 1 – p.

<^ZgghfkemqZ_ P = 1 − q 1 − p 2 (1 − q 2 ) .()1.9.()J_r_gb_ZgZeh]bqgh P = 1 − (1 − p 2 ) 1 − p (1 − q 2 ) .1.10.( (J_r_gb_ZgZeh]bqgh P = 1 − q 1 − 1 − (1 − p 2 )2)) = 1 − q (1 − p ) .2 21.11.( ())J_r_gb_ZgZeh]bqgh P = 1 − (1 − p 2 ) 1 − 1 − q (1 − p 2 ) = 1 − q (1 − p 2 ) .1.12.( ())J_r_gb_ZgZeh]bqgh P = 1 − q 1 − 1 − q (1 − p 3 ) = 1 − q 2 (1 − p 3 ).1.13.()J_r_gb_ZgZeh]bqgh P = 1 − q 1 − (1 − q 2 ) .21.14.J_r_gb_ZgZeh]bqgh P = p 2 (1 − q 2 ) .221.15.J_r_gb_ZgZeh]bqgh P = (1 − q 2 )(1 − q 3 ) .21.16.J_r_gb_ZgZeh]bqgh P = p 2 (1 − q 2 )(1 − q 3 ) .1.17.()J_r_gb_ZgZeh]bqgh P = p (1 − q 3 ) 1 − q (1 − p 2 ) .NhjfmeZiheghc\_jhylghklb2.1.Bf_xlky^\_mjgu<i_j\hcmjg_Z1[_euorZjh\bb1±qzjguoZ\h\lhjhcmjg_Z2[_euorZjh\bb2±qzjguoBadZ`^hcmjguba\e_dZxlihh^ghfmrZjmbi_j_deZ^u\Zxlbo\^jm]mxmjgmbai_j\hc\h\lhjmxba\lhjhc±\i_j\mxAZl_fbai_j\hcmjguba\e_dZxl[_a\ha\jZs_gbynrZjh\DZdh\Z\_jhylghklvqlhkj_^bgbohdZ`_lkym[_euo"4J_r_gb_ ih nhjfme_ iheghc \_jhylghklb p = ∑ p ( Ai ) p ( Bi ), ]^_ – ba\e_q_gb_ gZi =1i_j\hfwlZi_bamjg^\mo[_euorZjh\±[_eh]hbqzjgh]h±qzjgh]hb[_eh]h±^\moqzjguoAi – \_jhylghklvkhhl\_lkl\mxs_]hbkoh^ZgZi_j\hfwlZi_<i±gZ\lhjhfIhwlhfmCam1 ⋅ Cbn1− mCam1 −1 ⋅ Cbn1−+m1Cam1 +1 ⋅ Cbn1−−1ma1a2a1b2b1a2p=+++( a1 + b1 )( a2 + b2 ) Can1 +b1( a1 + b1 )( a2 + b2 ) Can1 +b1( a1 + b1 )( a2 + b2 ) Can1 +b1Cam1 ⋅ Cbn1− mb1b2+.( a1 + b1 )( a2 + b2 ) Can1 +b12.2.Bamjgu\dhlhjhcgZoh^ylkyZ1[_euorZjh\bb1qzjguom^Zeyxlh^bgrZjIhke_wlh]hbamjguba\e_dZxlihhq_jz^ghk\ha\jZs_gb_fnrZjh\DZdh\Z\_jhylghklvqlhkj_^bgbo[m^_lm[_euorZjh\"mn−ma1 Ca1 + m − 2 ⋅ Cb1 + n − m −1J_r_gb_ ih nhjfme_ iheghc \_jhylghklb ihemqbf p =+a1 + b1Can1 +b1 + n− 2mn−mb1 Ca1 + m −1 ⋅ Cb1 + n− m − 2+.a1 + b1Can1 +b1 + n− 22.3.Bf_xlky^\_mjgu<i_j\hcmjg_Z1[_euorZjh\bb1±qzjguo\h\lhjhcmjg_Z2[_euobb2qzjguoBadZ`^hcmjgum^Zeyxlihh^ghfmrZjmAZl_f\k_rZjuba\lhjhcmjgui_j_deZ^u\Zxl\i_j\mxbbag_zba\e_dZxl[_a\ha\jZs_gbynrZjh\DZdh\Z\_jhylghklvqlhkj_^bgbohdZ`_lkym [_euo"J_r_gb_ ih nhjfme_ iheghc \_jhylghklb+p=Cam1 + a2 − 2 ⋅ Cbn1−+mb2a1a2+( a1 + b1 )( a2 + b2 ) Can1 + a2 +b1 +b2 −2Cam1 + a2 −1 ⋅ Cbn1−+mb2 −1Cam1 + a2 −1 ⋅ Cbn1−+mb2 −1Cam1 + a2 ⋅ Cbn1−+mb2 − 2a1b2a2b1b1b2.++( a1 + b1 )( a2 + b2 ) Can1 + a2 +b1 +b2 − 2 (a1 + b1 )( a2 + b2 ) Can1 + a2 +b1 +b2 −2 ( a1 + b1 )(a2 + b2 ) Can1 + a2 +b1 +b2 −22.4.Bf_xlky^\_mjgu<i_j\hcmjg_Z1[_euorZjh\bb1qzjguo\h\lhjhcmjg_a2[_euorZjh\bb2qzjguoBai_j\hcmjguba\e_dZxlrZjZbi_j_deZ^u\Zxlbo\h\lhjmxmjgmAZl_fba\lhjhcmjguba\e_dZxlihhq_j_^ghk\ha\jZs_gb_fnrZjh\DZdh\Z\_jhylghklvqlhkj_^bgbohdZ`_lkym[_euorZjh\"Ca21 Cam2 + m +1 ⋅ Cbn2−+mn − m −1 a1b1 Cam2 + m ⋅ Cbn2−+mn − mCb21 Cam2 + m −1 ⋅ Cbn2 + n − m +1J_r_gb_: p = 2.+ 2+ 2Ca1 +b1Can2 +b2 + n+1Ca1 +b1 Can2 + b2 + n+1Ca1 +b1Can2 +b2 + n+12.5.

Bf_xlky^\_mjgu<i_j\hcmjg_Z1[_euorZjh\bb1qzjguo\h\lhjhcmjg_a2[_euorZjh\bb2qzjguo\lj_lv_cmjg_a3[_euorZjh\bb3qzjguoBai_j\uo^\mo mjgba\e_dZxlihh^ghfmrZjmbi_j_deZ^u\Zxlbo\lj_lvxmjgmAZl_fbalj_lv_cmjguba\e_dZxl[_a\ha\jZs_gbynrZjh\DZdh\Z\_jhylghklvqlhkj_^bgbohdZ`_lkym[_euorZjh\"J_r_gb_:Cam3 + 2 ⋅ Cbn3− mCam3 +1 ⋅ Cbn3−+m1Cam3 ⋅ Cbn3−+m2a1a2a1b2 + a2b1b1b2p=++.( a1 + b1 )( a2 + b2 ) Can3 +b3 +2 ( a1 + b1 )( a2 + b2 ) Can3 +b3 +2 ( a1 + b1 )( a2 + b2 ) Can3 +b3 +22.6.

< mjg_ gZoh^blky [_euo rZjh\ b qzjguo AZl_f \ mjgm ^h[Z\ey_lky rZjZijbqzfdZ`^uc^h[Z\ey_fucrZjg_aZ\bkbfhhlhklZevguok\_jhylghklvxphdjZrb\Z_lky\[_eucp\_lbk\_jhylghklvxq = 1 – p \qzjgucp\_lIhke_wlh]hbamjguba\e_dZxl[_a\ha\jZs_gbyrZjh\DZdh\Z\_jhylghklvqlhkj_^bgbohdZ`_lky[_euo"C7 ⋅C3C 7 C3C7 C3J_r_gb_ ih nhjfme_ iheghc \_jhylghklb p = p3 12 10 8 + p 2 q 1110 9 + pq 2 10 1010 +C20C20C20+ q3C97 C113.10C202.7.

<mjg_gZoh^blky[_euorZjh\bqzjguoAZl_fijhba\h^blkyqZklbqgZyaZf_gZrZjh\ke_^mxsbfh[jZahfdZ`^uc[_eucrZjg_aZ\bkbfhhl^jm]bok\_jhylghklvxphklZ\ey_lkygZf_kl_Zk\_jhylghklvxq = 1 – p hdjZrb\Z_lky\qzjgucp\_lIhke_wlh]hbamjgu ba\e_dZxl ihhq_jz^gh k \ha\jZs_gb_f rZjZ DZdh\Z \_jhylghklv qlh kj_^b gbohdZ`_lkyohly[uh^bg[_eucrZj"J_r_gb_Bkdhfh_kh[ulb_h[jZlghdba\e_q_gbxljzoqzjguorZjh\lh]^Zihnhjfm35k 5 − k C5 + k + 3−1 e_iheghc\_jhylghklb p = ∑ 1 − p q.C103 + 3−1 k =0 2.8. < mjg_ gZoh^blky [_euo rZjh\ b qzjguo DZ`^uc [_euc rZj g_aZ\bkbfh hl^jm]bok\_jhylghklvxp m^Zey_lkyba mjguZk\_jhylghklvxq = 1 – phklZ\ey_lky \g_cIhke_ wlh]h ba mjgu ba\e_dZxl ihhq_jz^gh k \ha\jZs_gb_f rZjZ DZdh\Z \_jhylghklvqlhkj_^bgbohdZ`_lkyohly[uh^bg[_eucrZj"5C3J_r_gb_ZgZeh]bqgh p = ∑ 1 − p k q5− k 3 5+3−1 .C10− k + 3−1 k =0 KemqZcgu_\_ebqbgu>bkdj_lgu_jZkij_^_e_gby[bghfbZevgh_]_hf_ljbq_kdh_IZkdZey3.1.Ijhba\h^ylNk_jbcih[jhkZgbcb]jZevghcdhklb\dZ`^hck_jbbDZdh\Z\_jhylghklvqlhjh\gh\kk_jbyo≤ k ≤ Nr_klvhqdh\\uiZ^_l[he__ljzojZa"J_r_gb_j1±\_jhylghklvlh]hqlhr_klvhqdh\\uiZ^_l[he__ljzojZaohly[u\h^10ghck_jbb3khklZ\ey_l92815 1 55p1 = 1 − q10 − pq 9 − p 2 q 8 − p 3q 7 = 1 −   −   −     −66 6 6671 5−     , ]^_±ihegZy\_jhylghklvZ\uqblZ_fu_±\_jhylghklb\uiZ^_gbyr_klbhq6 6dh\bebjZaZjZkkqblZggu_^ey^bkdj_lgh]hjZ\ghf_jgh]hjZkij_^_e_gby<_jhylghklv g_h[oh^bfh]h bkoh^Z jh\gh \ k k_jbyo fh`_l [ulv jZkkqblZgZ k ihfhsvx nhjfmeuN −k^ey[bghfbZevgh]hjZkij_^_e_gby P = C Nk p1k (1 − p1 ) .3.2.Ijhba\h^ylN g_aZ\bkbfuobkiulZgbcBkiulZgb_khklhbl\[jhkZgbyob]jZevghcdhklb^h\lhjh]hihy\e_gbyqbkeZhqdh\djZlgh]hljzfmki_ohfkqblZ_lky\lhjh_ihy\e_gb_mdZaZggh]h qbkeZ hqdh\ g_ iha`_ iylh]h [jhkZgby dhklb K dZdhc \_jhylghklvx ohly [u \h^ghfbaN g_aZ\bkbfuobkiulZgbcijhbahc^zlmki_o"J_r_gb_: p1±\_jhylghklvg_h[oh^bfh]hbkoh^Z\h^ghfbkiulZgbb_zfh`ghjZkkqb1lZlv ih nhjfme_ ^ey jZkij_^_e_gby IZkdZey  p =  .

p1 = C20+ 0 −1 ⋅ p 2 q 0 + C21+1−1 p 2 q1 +322 232 3222 22 3+C2+ 2−1 ⋅ p q + C2+ 3−1 ⋅ p q = p + 2 p q + 3 p q + 4 p q . G_h[oh^bfuc bkoh^ ohly [u \ h^ghfbkiulZgbb ± kh[ulb_ ijhlb\hiheh`gh_ hlkmlkl\bx wlh]h bkoh^Z \h \k_o bkiulZgbyo ihNwlhfm P = 1 − (1 − p1 ) .3.3.Ijhba\h^ylk_jbc[jhkZgbcfhg_lu^hi_j\h]hihy\e_gby]_j[Z\k_jbbDZdh\Z\_jhylghklvqlhjh\gh\k_jbyo]_j[\i_j\u_ihy\blkyijbk_^vfhf[jhkZgbbfhg_lu"J_r_gb_: j1 ± \_jhylghklv g_h[oh^bfh]h bkoh^Z \ h^ghc k_jbb jZkkqblu\Z_lky k ih1fhsvxnhjfmeu^ey]_hf_ljbq_kdh]hjZkij_^_e_gby p1 = pq 6 , ]^_p = q = bkdhfZy\_jh2851515ylghklv\uqbkey_lkyih[bghfbZevghcko_f_ P = C100 ⋅ p1 (1 − p1 ) .3.4.

Ijhba\h^yl k_jbc [jhkZgbc b]jZevghc dhklb ^h lj_lv_]h ihy\e_gby r_klb hqdh\DZdh\Z\_jhylghklvqlhr_klvhqdh\ihy\ylky\lj_lbcjZaijbk_^vfhf[jhkZgbbdhklbohly[u\h^ghcbak_jbc"J_r_gb_: p1±\_jhylghklvmdZaZggh]hkh[ulby\h^ghck_jbb^Zggu_bkiulZgbyhib341 5ku\ZxlkyjZkij_^_e_gb_fIZkdZeykn bk = 4: p1 = C34+ 4−1 ⋅ p 3 q 4 = C64     . <_jhyl6 6ghklv ihy\e_gby gm`gh]h bkoh^Z ohly [u \ h^ghc ba k_jbc ± kh[ulb_ ijhlb\hiheh`gh_ d20hlkmlkl\bxwlh]hbkoh^Z\h\k_ok_jbyolh_klv P = 1 − (1 − p1 ) .3.5.Ijhba\h^yl k_jbx g_aZ\bkbfuo bkiulZgbc ^h ihy\e_gby i_j\h]h mki_oZ DZ`^h_bkiulZgb_ khklhbl \ n [jhkZgbyo b]jZevghc dhklb mki_ohf ijb wlhf kqblZ_lky \uiZ^_gb_ohly[uh^bgjZaljzobebq_lujzohqdh\DZdh\Z\_jhylghklvqlhmki_o\i_j\u_ijhbahc^zl\h^bggZ^pZlhfbkiulZgbbk_jbb"J_r_gb_mki_oh^gh]hbkiulZgby±kh[ulb_ijhlb\hiheh`gh_dhlkmlkl\bxmki_oZnn2jZalh_klv p1 = 1 −   ±\_jhylghklvmki_oZh^gh]hbkiulZgby>eyhij_^_e_gbybkdhfhc3\_jhylghklbijbf_gbfnhjfmem]_hf_ljbq_kdh]hjZkij_^_e_gby P = p1 (1 − p1 ) .103.6.

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Тип файла PDF

PDF-формат наиболее широко используется для просмотра любого типа файлов на любом устройстве. В него можно сохранить документ, таблицы, презентацию, текст, чертежи, вычисления, графики и всё остальное, что можно показать на экране любого устройства. Именно его лучше всего использовать для печати.

Например, если Вам нужно распечатать чертёж из автокада, Вы сохраните чертёж на флешку, но будет ли автокад в пункте печати? А если будет, то нужная версия с нужными библиотеками? Именно для этого и нужен формат PDF - в нём точно будет показано верно вне зависимости от того, в какой программе создали PDF-файл и есть ли нужная программа для его просмотра.

Список файлов книги