L_fZ Bkke_^h\Zgb_g_iZjZf_ljbq_kdh]hZe]hjblfZjZkihagZ\Zgby h[gZjm`_gby h[jZah\gZ[ex^Z_fuoq_eh\_dhf-hi_jZlhjhf...
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L_fZ Bkke_^h\Zgb_g_iZjZf_ljbq_kdh]hZe]hjblfZjZkihagZ\Zgby h[gZjm`_gby h[jZah\gZ[ex^Z_fuoq_eh\_dhf-hi_jZlhjhfgZ nhg_ihf_o P_evjZ[hlu Mq_[gZy–bamq_gb_hkgh\guowe_f_glh\ f_lh^bdijh\_^_gbywdki_jbf_glh\kq_eh\_dhf-hi_jZlhjhf, GZmqgZy–ihbkdkljmdlmjunhjfmeu hibku\Zxs_caZ\bkbfhklv\_jhylghklbh[gZjm`_gbyh[jZaZhl bgl_gkb\ghklbihf_obbiZjZf_ljh\,oZjZdl_jbamxsbo bg^b\b^mZevghklvq_eh\_dZ\wlhf\b^_^_yl_evghklb Ebl_jZlmjZ 1. ;Zj^bgD< Ijh[e_fZihjh]h\qm\kl\bl_evghklbbikbohnbabq_kdb_f_lh^u –F: GZmdZ 2. E_\bg;J L_hj_lbq_kdb_hkgh\uklZljZ^bhl_ogbdbLhf, -FKh\JZ^bh 1976. ;m^dh<GDe_f_glv_\NFGh\bdh\ZGF G_iZjZf_ljbq_kdZyfh^_evh[gZjm`_gbykb]gZeh\ gZ[ex^Z_fuoq_eh\_dhf-hi_jZlhjhfgZnhg_rmfh\ JZ^bhl_ogbdZbwe_dljhgbdZ-lL 1. ;hevr_\EGKfbjgh\G< LZ[ebpufZ_fZlbq_kdhcklZlbklbdb–F:GZmdZ L_hj_lbq_kdZyqZklv Ki_pbnbdZdZdnbabq_kdbooZjZdl_jbklbdq_eh\_dZhi_jZlhjZ\kbkl_f_q_eh\_d-fZrbgZlZdbnmgdpbhgZevguo oZjZdl_jbklbd_]h^_yl_evghklb\wlhckbkl_f_khklhbl\lhfqlh\ [hevrbgkl\_kemqZ_\dhebq_kl\_ggu_\_ebqbguwlbooZjZdl_jbklbd y\eyxlkyihjh]h\ufbb\_jhylghklgufbWlZhkh[_gghklv hij_^_ey_lk\hxf_lh^bdmijh\_^_gbywdki_jbf_glh\kq_eh\_dhfhi_jZlhjhf[1]. <[2] ^Z_lkyl_hjbyZ\lhfZlbq_kdbog_iZjZf_ljbq_kdbo h[gZjm`bl_e_ckb]gZeZG_iZjZf_ljbq_kdbfgZau\Zxl h[gZjm`bl_evkb]gZeZ_kebhgh[_ki_qb\Z_lihklhyggmx \_jhylghklveh`ghclj_\h]bijb^hklZlhqghkeZ[uoh]jZgbq_gbyo gZklZlbklbq_kdb_oZjZdl_jbklbdb\oh^guokb]gZeh\
HibkZggu_\[2]jZ[hqb_oZjZdl_jbklbdbZ\lhfZlbq_kdbo g_iZjZf_ljbq_kdboh[gZjm`bl_e_cBkihevamxsbo^ey h[gZjm`_gbykb]gZeZeb[hagZdh\u_eb[hjZg]h\u_eb[hagZdh\hjZg]h\u_klZlbklbdbfh`ghh[h[sblvbij_^klZ\blv\\b^_ : ρ1−β=ρα+a*H/σ (1) ]^_: ρ1−β –\_jhylghklvijZ\bevgh]hh[gZjm`_gby\ujZ`_ggZy\ d\ZglbeyoghjfZevgh]hjZkij_^_e_gby ρα –\_jhylghklveh`ghclj_\h]b a/σ –hlghr_gb_kb]gZe/ rmf H –dhwnnbpb_glaZ\bkysbchlZe]hjblfZjZ[hlu h[gZjm`bl_ey\b^Zkb]gZeZbihf_ob DeZkkbnbdZpbyj_r_gbcijbgbfZ_fuoh[gZjm`bl_e_f ijb\_^_gZ\lZ[ebp_: Kb]gZe J_r_gb_h[gZjm`bl_ey H[hagZq_gb_\_jhylghklbkh[ulby _klv G_lkb]gZeZ Hrb[dZijhimkdkb]gZeZρ10 g_l G_lkb]gZeZ IjZ\bevgh_j_r_gb_ρ00 _klv ?klvkb]gZe IjZ\bevgh_j_r_gb_ρ11 g_l ?klvkb]gZe Hrb[dZeh`gZylj_\h]Zρ01 H[hagZqbfijZ\bevgh_h[gZjm`_gb_ρih ≡ ρ00+ρ11 eh`gZylj_\h]Zρel ≡ ρ01 <>@ihdZaZghqlhijbh[gZjm`_gbbq_eh\_dhf—hi_jZlhjhf JEKkb]gZeZgZ[ex^Z_fh]hgZnhg_rmfh\gZbg^bdZlhj_lbiZ“A”, _]hjZ[hqZyoZjZdl_jbklbdZbf__lkljmdlmjmnhjfmeu Ijbwlhf dhwnnbpb_gl “G”–_klvoZjZdl_jgZy^eyq_eh\_dZ—hi_jZlhjZ \_ebqbgZ Bg^bdZlhjlbiZ“A”–wlhh^ghf_jgucbg^bdZlhjHlf_ldZ kb]gZeZijhkfZljb\Z_lkygZaZrmfe_gghcebgbbjZa\_jldb we_dljhggh–emq_\hcljm[db\\b^_bkdZ`_ggh]hdhehdhehh[jZagh]h bfimevkZjbk <^ZgghcjZ[hl_baf_jyxlky\_jhylghklbρih ijZ\bevgh]h h[gZjm`_gby^\mf_jguoijhkluoh[jZah\gZijbf_jdZjlbghdlbiZ
khklZ\e_gguobaklbebah\Zgguowe_f_glh\b gZ[ex^Z_fuohi_jZlhjhfgZ“aZ[blhf”ihf_oZfbwdjZg_L<-^bkie_y W
Knhjfbjh\Zggh_Weywlh]h baf_jyxlkyaZ\bkbfhklb\_jhylghkl_cijZ\bevgh]hh[gZjm`_gbyρih beh`ghclj_\h]bρelhlaZrmfe_gghklbnhgZρad nbh[jZaZρad h[j, ijbaZ^Zgghckljmdlmj_rmfZ Bah[jZ`_gb_nhjfbjm_lkyijh]jZfghGZwdjZg_L<-^bkie_y Wey ]jZnbq_kdh]hj_`bfZjZ[hluWeykbf\hevgh]h^bkie_y[m^_f\dZq_kl\_ we_f_glZbah[jZ`_gbybkihevah\ZlvagZdhf_klhkbf\heZ Bah[jZ`_gb_[m^_ljbkh\Zlvkyijh[_eZfbbih^oh^ysbfb kbf\heZfbgZijbf_j beb[md\hc“O”<h[hbokemqZyolZdb_ fbgbfZevgu_^bkdj_lubah[jZ`_gby[m^_fgZau\Zlvwe_f_glZfb wdjZgZBah[jZ`_gbyh[jZah\^_ebfgZfhghkljmdlmgu_– gZjbkh\Zggu_dZd[udbklvxihklhygghclhesbgub ihebkljmdlmjgu_–gZjbkh\Zggu_dbklyfbjZaghclhesbgujbk >Ze__[m^_fbkihevah\Zlvlhevdhfhghkljmdlmjgu_bah[jZ`_gby >eyhibkZgbykljmdlmjubah[jZ`_gbch[jZaZbihf_obrmfZ bkihevam_fke_^mxsb_iZjZf_lju: 1)iehsZ^vkljmdlmjgh]hwe_f_glZbah[jZ`_gbygZijbf_j:
Sh[j=1, Sh[j=2*2, Sh[j Kljmdlmjgu_we_f_glubah[jZ`_gby \k_]^Zd\Z^jZlgu_ iehsZ^vkljmdlmjgh]hwe_f_glZbah[jZ`_gbyrmfZ: Sr=1, Sr=2*2, Sr bl^ dhebq_kl\hkljmdlmjguowe_f_lh\h[jZaZjbk <^ZgghcjZ[hl_jZkihagZ\Zgb_f_klZjZkiheh`_gby h[gZjm`b\Z_fh]hh[jZaZg_\oh^bl\aZ^Zqmhi_jZlhjZIhwlhfm h[jZa^eyh[gZjm`_gbyke_^m_ljZkiheZ]Zlv\h^ghfblhf`_f_kl_ wdjZgZba\_klghfhi_jZlhjm–\p_glj_jZ[hq_]hihey >eynhjfbjh\ZgbyjZ[hq_]hkgZqZeZih\_jhylghklb ρh[j ijbgbfZ_lkyj_r_gb_[m^_lebbah[jZ`_gb_h[jZaZijbkmlkl\h\Zlv \^Zgghcj_ZebaZpbbdZjlbgdbjZ[hq_]hiheyAZl_fdZ`^ucwe_f_gl jZ[hq_]hiheyaZdjZrb\Z_lkyi_qZlZ_lky[md\Zbebibdk_e bebg_l ihke_^mxs_fmijZ\bem ?kebgZ^Zgghfwe_f_gl_wdjZgZbah[jZ`_gbyh[jZaZg_ ^he`gh[ulvwe_f_glnhgh\uc lhhgaZdjZrb\Z_lkyk \_jhylghklvxρad n ?keb^Zggucwe_f_glwdjjZgZ\oh^bl\bah[jZ`_gb_h[jZaZb h[jZaijbkmlkl\m_l\^Zgghcj_ZebaZpbblhwe_f_glwdjZgZ aZdjZrb\Z_lkyk\_jhylghklvxρad h[j IjbwlhfkljmdlmjZrmfZmqblu\Z_lkylZd?kebSr lh\k_ we_f_gluwdjZgZih^\_j]Zxlky\ha^_ckl\bxrmfZg_aZ\bkbfh?keb Sr=2*2 b[he__lhwe_f_gluwdjZgZihiZ\rb_\gmljvd\Z^jZlZ we_f_glZrmfZaZdjZrb\Zxlkybebg_lkh\f_klghh^ghchi_jZpb_c jhau]jurZ\_jhylghklb
H[eZklbbaf_g_gby Pad nbPad h[j .
<_ebqbgu\_jhylghl_cρad h[j bρad h[j. aZrmfe_gghklbjZ[hq_]hihey hij_^_ey_lkydhgdj_lghcnbabq_kdhcfh^_evx\ha^_ckl\byrmfZgZ bah[jZ`_gb_
1). hlghr_gb_fkb]gZeihjh]D9 hlghr_gb_fihjh]rmf: V/σx , eb[hkb]gZe/rmf: Z/σx nmgdpb_cjZkij_^_e_gbyrmfZϕ(x) k^bki_jkb_cσx2 b gme_\uffZlh`b^Zgb_f >Ze__[m^_fjZkkfZljb\Zlvrmfbf_xsbcghjfZevgh_ jZkij_^_e_gb_ >eylh]hqlh[u^eykemqZcghc\_ebqbguZobf_xs_c ^bki_jkbxσx2b X Zihevah\ZlvkynhjfmeZfbbeblZ[ebpZfb klZg^Zjlgh]hghjfZevgh]h jZkij_^_e_gbykemqZcghc\_ebqbguN01 c σN b N = 0 1
ϕ(N01)=
exp[–N012/2]
2π
gZ^hkemqZcgmx\_ebqbgmZop_gljbjh\ZlvdZbghjfbjh\Zlvd σx Lh]^Zk\yavnmgdpbbjZkij_^_e_gbykmffuZok\_ebqbgZfb Zb9[m^_llZdZydZdgZjbkZ\_jhylghklbaZdjZrb\Zgby hij_^_eylkybgl_]jZeZfb ∞
z2 − 2
V 1 PN01 > = e dz ∫ ρad n= σx 2π V σ
(4)
x
∞ z − V − a 1 2 > = P N e dz ∫ ρad h[j= 01 σ 2π V−a x σ 2
(5)
x
Banhjfme b \b^ghqlh: 0 < Pad n=< 0,5
V →∞ σx
V →0 σx
ρad h[j >= ρad n
B\k_]^Z
>eyZ > V: ρad h[j V −a < −(3 ÷ 5) σx
→ijbσo → ijZdlbq_kdbijb
V −a > (3 ÷ 5) σx <_ebqbgZ\_jhylghklbPh[j\u[bjZ_lkybkoh^ybaf_lh^bdb ijh\_^_gbywdki_jbf_glZ >eyZ < V: ρad h[j
→ijbσo → ijZdlbq_kdbijb
F_lh^bdZihlhq_qgh]hbaf_j_gby GZqZevgu_mkeh\by3ad n, Pad h[j, (
V V −a ), ( ) bkljmdlmjZ σx σx
Sr H^gZbawlbo\_ebqbgy\ey_lky\ZjbZglhc S h[j Zj]mf_glhf bkdhfhcaZ\bkbfhklbhklZevgu_\_ebqbgu–aZ^Zggu_ dhgklZglu Nhjfbjm_lkyF~(30 ÷100) ij_^ty\e_gbcj_ZebaZpbc dZjlbgdbjZ[hq_]hihey^eyi_j\h]hagZq_gby\ZjbZglu Nbdkbjmxlkyj_amevlZluijbgylbyj_r_gbyhi_jZlhjhfbih nhjfmeZf \uqbkeyxlky\_ebqbguρih bρell_gZoh^blkyi_j\Zy lhqdZbkdhfhcaZ\bkbfhklb AZl_f[_jzlky\lhjh_agZq_gb_\ZjbZglubkgh\Z^ZzlkyF ij_^ty\e_gbcknhjfbjh\Zgguoih\_jhylghklbdZjlbghd IhemqZ_lkyke_^mxsZy–\lhjZylhqdZdjb\hcbl^>eywlhc f_lh^bdb3h[j=0,5. rmfZ
F_lh^bdZ]jmiih\h]hbaf_j_gby GZijbf_jieZgbjm_lkyihemqblvdjb\mxaZ\bkbfhklb: ρih=f(
S r a V =const, S h[j V σx ↑
\ZjbZglZ
=const)
iZjZf_lju djb\hc
L_i_jvwdki_jbf_glkhklhblbaFh[sij_^ty\e_gbckj_^b dhlhjuo^he`ghkh^_j`ZlvkyDk_jbcihFdd «D ij_^ty\e_gbcj_ZebaZpbcbah[jZ`_gbyjZ[hq_]hiheykh^_j`Zs_]h h[jZakaZ^Zggufd–fagZq_gb_f
a K . ∑ M k = M V k =1
Weylh]hqlh[u\uqbke_gbyihnhjfme_ bf_eb h^bgZdh\mxlhqghklvgZ^hqlh[udZ`^Zyk_jbybf_eZh^bgZdh\h_
dhebq_kl\hij_^ty\e_gbcFd K FRQVWghqlh[uij_^ty\e_gby kemqZcghq_j_^h\ZebkvbajZaguok_jbcDjhf_lh]hgZ^h_sz h[_ki_qblvqlh[uqZklvij_^ty\e_gbcg_kh^_j`ZeZh[jZaZ L_i_jvfh`gh\aylvPh[jf_gvr_Bih\b^bfhfm ikboheh]bq_kdb\hkijbylb_kemqZcghklbihy\e_gbyg_ihy\e_gby h[jZaZkhojZgblkymhi_jZlhjZijbmf_gvr_gbbPh[j\iehlv^h \_ebqbgu.qlhiha\heblagZqbl_evghkhdjZlblvh[s__\j_fy wdki_jbf_glZ >eyj_ZebaZpbbmdZaZgguolj_[h\Zgbcfh`ghij_^eh`blv gZijbf_jke_^mxsbcZe]hjblfnhjfbjh\Zgbyij_^ty\e_gbc “Hj]ZbaZpby fZkkb\Z ba D kqzlqbdh\ qbkeZ ^ey i hl 0 ^hD gp M[i] := C ij_^ty\e_gbc \ dZ`^hc k_jbb b aZg_k_gb_ \ dp dZ`^uc kqzlqbd bkoh^gh]h qbkeZ K ^ey i hl 0 ^hD “<\h^ fZkkb\Z ba D gZqZevguo agZq_gbc a/V. gp \\h^ P[i] dp _keb {kemqZcgh_qbkeh[0,1]}>1/K lhb^lbf_ldZ bgZq_b^lbf_ldZ \kz_keb Fih^ijh]jZffZ nhjfbjh\Zgby bah[jZ`_gby jZ[hq_]h ihey [_a h[jZaZ FL :={kemqZcgh_qbkeh[0,1]} “kemqZcguc \u[hj agZq_gby Jad h[j , gZijbf_j ijb D L := INT(L*10) “INT–p_eZy qZklv qbkeZ _keb M[L] = 0 lhb^lbf_ldZ \kz_keb M[l ]:=M[L]–1 Pad h[j:=P[L] ih^ijh]hjZffZnhjfbjh\Zgby bah[jZ`_gby jZ[hq_]h ihey kh^_j`Zs_]h h[jZa
k Jad h[j=P[L].
Ih^]hlh\dZdjZ[hl_ – KhklZ\blvf_lh^bdm\uiheg_gby\u[jZggh]h\ZjbZglZ eZ[hjZlhjghcaZ^Zqb – Hij_^_eblvh[eZklvbaf_g_gbybqbkehlhq_dgZqZevguomkeh\bc – KhklZ\blv^eywlh]h\ZjbZglZijh]jZffmjZ[hluW
–fh^mevnhjfbjh\Zgbyj_ZebaZpbbbah[jZ`_gbyjZ[hq_]h ihey –fh^mev^bZeh]ZWeybkdexq_gbyjZkk_ygby\gbfZgbyhi_jZlhjZdZ`^Zyk_jby ij_^ty\e_gbchlebqZxsZykybkoh^gufbmkeh\byfb^he`gZ ijh^he`Zlvkyg_[he__–fbgkihke_^mxsbfi_j_ju\hf–5 fbg Ke_^m_l\\_klbij_^\Zjbl_evgmxk_jbx^eyh[mq_gby hi_jZlhjZbklZ[bebaZpbb_]hjZ[hluWlZk_jby\ijhlhdhe_ j_amevlZlh\bkke_^h\Zgbyg_nbdkbjm_lky Ihihemq_gguf^Zggufkljhylkydjb\u_aZ\bkbfhkl_cJihb JelhlgZqZevguomkeh\bcbijhba\h^blkybokjZ\g_gb_knhjfmehc (1). Bg^b\b^mZevgu_\ZjbZglueZ[hjZlhjguoaZ^Zq 6.1
H[jZa:
6.2 6.3 6.4 6.5
Sh[j=5, Sr=1, Sr/ S ÷ h[j=1, V/σx= var =0.1 ÷ 3 a/V= const =0.5 H[jZalhl`_a/V= const =1.1 H[jZalhl`_a/V= const =2 H[jZalhl`_a/σx= var =0.1 ÷ 3, V/σx= const =0.1 H[jZalhl`_ V/σx= const =1
6.6–Lh`_qlh–gh^eyh[jZaZ: Ijbeh`_gb_ Bgl_]jZe: ∞
Q(y)=1/
2π ∫ e
− z2 2
dz
y
Fh`ghgZclbihlZ[ebpZf[4],eb[h\uqbkeblvjZaeh`_gb_f\jy^ :e]hjblf>ey =< y >= 3 y
P(y)= 1/ 2π ∫ e
−t 2 2
−∞ ∞
Q(y)= 1/ 2π
∫e
−t 2 2
2
dt = 0.5–1/ 2π e
y
1:
y 2n+1 1⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ (2n +1)
dt = 0.5+1/ 2π e−y / 2 ⋅ ∑ − y2 / 2
y 2n+1 ⋅∑ 1⋅ 3 ⋅ 5 ⋅ ⋅ ⋅ (2n +1)
\\h^< z := exp(–Y*Y/2)/sqr(2*π) r := 1 s := 0 n := 0 k := 2*n+1 r :=r*k w := s s := s+(Yk)/r n :=n+1 _kebs–w >= 10–10 lh goto 1 bgZq_ P := 0.5+z*s Q := 0.5–z*s
Lhqghklv\uqbke_gbcm\_ebqb\Z_lkyijbmf_gvr_gbbY LZ[ebpZ: Y PjZkkqblZggu_ JlZ[ebqgu_ 0,01 0,50398936 0,503989 0,1 0,53982784 0,539828 1 0,84134775 0,841345
3
0,9986501
0,99866501
IJH=J:FF: 10 20 30 40 50 60 70 80 90
INPUT “Y=”; Y LET Z = EXP(–Y*Y/2)/SQR(2*PI) LET R = 1 : LET S =0 : LET N = 0 : LET W = S LET K = 2*N+1 : LET R = R*K LET S = S+(Y ↑ K)/R : LET N = N+1 IF S–W >= 1E–10 THEN GOTO 40 LET P = 0.5+S*Z PRINT “Y=”; Y ; TAB2 ; “P=”; P ; TAB2 ; “Q=”; 1–P GOTO 10
>eyY > wlhlZe]hjblfg_jZ[hlZ_lldqbkehrlj_[m_lky [hevr_^himklbfh]h^eyjZajy^ghck_ldbWey Y > 0 y
F(y) = 1/ 2π ∫ e 0
−t 2 2
3 5 dt =1/ 2π y − y + y 2
i=
0
y7 + ... 2 ⋅1!⋅3 2 ⋅ 2!⋅5 23 ⋅ 3!⋅7
1
2
−
3
A3 A0 A1 A2 H[hagZqbfghf_jZi = 0,1,2,… qe_gh\jy^ZA0,A1,A2,A3… y 2 i+1 y2 , B = –B , n = 1,2,3,… n n–1 2n 2 i ⋅ i! B An= n , A0 = y, B0 = y 2n + 1
Bi =
1:
\\h^Y a := Y b := Y s := Y n := 0 n := n+1 b := –b*(x2)/(2*n) a := b/(2*n+1) s := s+a _keb lhgoto 1 bgZq_
F := s/sqr(2*π) Q := 0.5–F Lhqghklv\uqbke_gbyJm\_ebqb\Z_lkyijbmf_gvr_gbbY. LZ[ebpZ Y PjZkqzlgu_ JlZ[ebqgu_ 0,5 0,69146246 0,691462 1 0,84134475 0,841345 3 0,9986501 0,9986501 4.5 0,99999676 0,9999966023 5 1,0000007 0,99999971335 IJH=J:FF: 10 20 30 40 50 60 70 80 90 100 110 120
INPUT “Y=”; Y LET A = Y : LET B = Y : LET S = Y LET N = 0 LET N = N+1 LET B = –B*(X ↑ 2)/(2*N) LETA = B/(2*N+1) LET S = S+A IF ABS(A) >= 1E–10 THEN GOTO 40 LET Q = S/SQR(2*PI) LET Q = 0.5+Q PRINT “Y=”; Y, “Q=”; Q GOTO 10
:e]hjblf: Lhqghklv\uqbke_gbyQihZe]hjblfZfbaZf_lgh mf_gvrZ_lkyijb[hevrboY. >eyY > 2lhqgu_\uqbke_gbyh[_ki_qb\Z_ljZaeh`_gb_ bgl_]jZeZ\_jhylghkl_c\p_igmx^jh[v ∞
Q(y)= 1/ 2π
∫e y
−t 2 2
e−y ⋅ 2π y + 2
dt =
\\h^F \\h^Y z := Y pbde^eyN = M ^hrZ]–1
1 1 y +
2 y +
3 y +
4 y + ...
z := Y+z /N dhg_ppbdeZ Q := EXP(–Y*Y/2)/SQR(2*π)/z P := 1–Q Lhqghklv\uqbke_gbyQihwlhfmZe]hjblfmaZf_lgh mf_gvrZ_lkyebrvijbY < 0,5. F \j_fykqzlZk Y PjZkqzlgh_ JlZ[ebqgh_ 0,1 0,53804137 0,2 0,57925653 0,3 0,61791142 F \j_fykqzlZk Y PjZkqzlgh_ JlZ[ebqgh_ 0,1 0,53969777 0,539828 0,2 0,57925969 0,579260 0,3 0,6179142 0,617911 IJH=J:FF: 10 20 30 40 50 60 70 80 90
INPUT “M=”; M INPUT “Y=”; Y LET Z = Y FOR N = M TO 1 STEP –1 LET Z = Y+N/Z NEXT LET Q = EXP(–Y*Y/2)/SQR(2*PI)/Z PRINT “Y=”; Y ; TAB2 ; “Q=”; Q ; TAB2 ; “P=”; 1–Q GOTO 20