Page 141 - الرياضيات المتقدمة كتاب الطالب الصف 12 الفصل 2

{Oz Gb Py3s b Æ kf b .&sb b Gb ^ Æ{j b {6 1.b d?Wb ç 2;N {j b X?cb f.[ gb Ÿ zB y2b

˜“½’ ^= : C;;8:= – Õ 06; CÕ=g±b/ ±ÕR=5 ½ ÐC ±º¯ y
› W:^ 5
^= : C;;8:= – Õ 0 CÕ=g±b/ ±ÕR=5 ½ ÐC ±º¯ y

˜“¿’ –“½’ –“Ã’ E90 E=g±b/ ´±R=5 E Ô»±R8 ± Z ¼b ± ÑC ¹­ ÎÒ±P ± `Û=

:›¢ c ¯  ` ³R 6 ± d “Ã’ R=5 :9 E:= ›œ P b ˜] º R= Ò­ –“² ½ ­’ Ò­ “² ½ ­’
›¢ à ›Ÿ ›Ÿ à ›œ ›œ à £ £ à à  Ã
zNy Fa vj&jfa
»±R8 ±
œž œ¡ œž œ¡ œž “´’ E C ¹b:4 ± ÃC6 »± ^Û : G= –Ô»±R8 ± ¶»P: ± d ^0 : ± dg±b/4 ± R=5 : ± ´C C= ÀR `8:

¢ = œž E C ˜C< ±»±R8 Z ³P: M± ´C C D C; Ò –»±R8 ±
 - »±R8 ±
˜´C C= ± »±R8 Ãb: : CÕ ÒC ³P: M± ´C C Ãb: Ðb8 –Ô»±R8 ± ¶»P: ± d
œœ c ¯ œ ` ³R 6 ± d “½’ R=5 :9 E:= œ› P b ˜Ô»±R8 ± ¶»P: ± ^8 c9 P: 4 c; ; _ R –^0 : ± dg±b/4 ± R=5 :9 d C: „± Z ¼b ± ^Û= :

œœ ½ ›¢ ›¢ ½ ›ž ›ž ½ ›š ›š ½ ½ œ ½ .probability density function (PDF) ÎC: „± E C E ±¹ Ê c; ;: ± ^= : c: Ù
»±R8 ±
›œ Ÿ ¢š Ÿ ›œ “´’ E C c ¯ »±R8 ± E C ÎÛb C; A –Ô»±R8 ± ¶»P: ± Ìb ÎC: „± E C E ±¹ c; ; _ R C P;
˜± Õ P ±Ò ÔÒC Ò –´„C: „± Ãb: : E ÒC c; ;: ± F E=98 ± E C : ± Ðb8 a=9 Ò –ÎC: „±
 = ›œ E C
œ - »±R8 ± b C: “½’ ^0 : ± dg±b/4 ± R=5 :9 Ô»±R8 ± ¶»P: ± Ìb ÎC: „± E C E ±¹ ´C=; ; _ R

œ c ¯ › ` ³R 6 ± d “¿’ R=5 :9 E:= ¢Ÿ P b ¤E= Š± ÎC8 M± d `Û=

ÎÑÎ ¿ ﻂﺳﻮﻟا ÎÑÍ
œ ¿ œ›œ› ¿ › › ¿ ›› ›› ¿ ¿ › ﻂﺳﻮﻟا ﻂﺳﻮﻟا
ﻂﻴﺳﻮﻟا ﻂﻴﺳﻮﻟا ﻂﻴﺳﻮﻟا
»±R8 ± لاﻮﻨﳌا لاﻮﻨﳌا لاﻮﻨﳌا لاﻮﻨﳌا لاﻮﻨﳌا لاﻮﻨﳌا لاﻮﻨﳌا
لاﻮﻨﳌا
œŸ ›Ÿ Ÿ ›Ÿ œŸ (ج) (ج) (ج) (ب) (ب) (ب) (أ) لاﻮﻨﳌا (أ) (أ)
“´’ ﻂﻴﺳﻮﻟا ﻂﻴﺳﻮﻟا ﻂﻴﺳﻮﻟا ﻂﻴﺳﻮﻟا ﻂﻴﺳﻮﻟا ﻂﻴﺳﻮﻟا
Ÿ = œŸ E C ﻂﺳﻮﻟا ﻂﺳﻮﻟا ﻂﺳﻮﻟا ﻂﺳﻮﻟا ﻂﺳﻮﻟا ﻂﺳﻮﻟا
› - »±R8 ± لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ لﺎﻤﺘﺣﻻا ﺔﻓﺎﺜﻛ

˜_=7 ± »±R8 E C D Ð? C<9: ­Ò –ÎÒ±P ± O ± “›

˜E ± ´C4 ¼b ± ` Û^8 CÕ »±R8 C Õ »P _ »± “œ ،ﺐﺟﻮﻣ ءاﻮﺘﻟا ،ﺐﺟﻮﻣ ءاﻮﺘﻟا ﻞﺛﺎﻤﺘﻣ ﻞﺛﺎﻤﺘﻣ ﻞﺛﺎﻤﺘﻣ ،ﺐﻟﺎﺳ ءاﻮﺘﻟا ،ﺐﻟﺎﺳ ءاﻮﺘﻟا
،ﺐﺟﻮﻣ ءاﻮﺘﻟا
،ﺐﻟﺎﺳ ءاﻮﺘﻟا
˜Ô»±R8 ¶»P Û^8 ³P: M± Ìb c; ; _ »± “ ﲔﻤﻴﻟا ﻰﻟإ ءاﻮﺘﻟﻻا ﲔﻤﻴﻟا ﻰﻟإ ءاﻮﺘﻟﻻا رﺎﺴﻴﻟا ﻰﻟإ ءاﻮﺘﻟﻻا رﺎﺴﻴﻟا ﻰﻟإ ءاﻮﺘﻟﻻا
ﲔﻤﻴﻟا ﻰﻟإ ءاﻮﺘﻟﻻا
رﺎﺴﻴﻟا ﻰﻟإ ءاﻮﺘﻟﻻا
©C< : » d ± E ± ´C=; ;: ± `= ÍR /: ± C “ž
«±b ± b “¶’ ^8/ ± d Z ¼b ± –^ C: “²’ ^8/ ± d Z ¼b ± «±b ± b “­’ ^8/ ± d Z ¼b ±
©d4= 2 ± c; ;: C a6jÒ `8: C< : » d ± ´C=; ;: ± Ô­ “Ÿ
R=5 :9 d C ± X b ± ÐM D b –d C ± X b ±Ò –αb;: ± Z7 Ò R=5 :9 d C ± X b ± ÐM D C

˜c; ;: ± E: `=: c ¯ Z7 “½’ –c; ;: ± E: P; X= b ±Ò ˜c; ;: ± E: »C c ¯ Z7 “½’
b Ò –^ C: “½’ ^0 : ± dg±b/4 ± R=5 :9 Ô»±R8 ± Z ¼b ± –› û/8 ± ÁC/ d
αb;: ± X= b ± d C ± X b ± ˜E ÒC C<4=: Ò Î±b;: ± X= b ± d C ± X b ±

˜½R ± ^8 Q ? d4= c; ;
αb;: ± § X= b ± § d C ± X b ±
` ¹P ¹P4 ^0 : ± dg±b/4 ± R=5 :9 d C: „± Z ¼b ± ^= : ÐC8 ˆC ÐC ±º¯
¤ÐA –³¹P ³R c9 d4= c; ;: _=7 ±
c ¯ c; ;: ± F E C : ± _ 7 d ± E:=7 ± P; X= b ± Z7 Ò c; ;: ± E: P; αb;: ± Z7
»b C< R: d ± E27; ± d Ò –“Ò’ d C ± X b ± P; Z7 d4= 2 ± c; ;: ± E: y

˜^ C: ± ˜`=Ø ÒC ` ­S
Û
˜Î±b;: ± § X= b ± § d C ± X b ± y .normal curve d4= 2 ± c; ;: ± ¤c: “²’ ^8/ ± d d C: „± Z ¼b ± ^Û : ÔQ ± c; ;: ±

11-038 MOE book 33.indd 140 25/12/2023 4:36 PM