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tr t trr t t - - PowerPoint PPT Presentation

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tr t trr t t Prt r trs rtt tts

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SLIDE 1

■♥tr♦ t♦ ❈♦♥t❡♠♣♦r❛r② ▼❛t❤

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s

❉❡♣❛rt♠❡♥t ♦❢ ▼❛t❤❡♠❛t✐❝s ❯❑

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SLIDE 2

❆♥♥♦✉♥❝❡♠❡♥ts

◮ ❆ ❤♦♠❡✇♦r❦ ❛ss✐❣♥♠❡♥t ✐s ❞✉❡ ♥❡①t ▼♦♥❞❛②✳ ◮ ❊①❛♠ ✷ ✐s ♥❡①t ❲❡❞♥❡s❞❛②✳

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SLIDE 3

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡♠✐♥❞❡rs

❯s❡ ❝♦♥t✐♥✉♦✉s ♣r♦❜❛❜✐❧✐t② ✇❤❡♥ ♣✐❝❦✐♥❣ r❛♥❞♦♠ r❡❛❧ ♥✉♠❜❡rs✳

◮ ❙❛♠♣❧❡ s♣❛❝❡s ❛♥❞ ❡✈❡♥ts ❛r❡ ♠❛❞❡ ✉♣ ♦❢ ✐♥t❡r✈❛❧s✳ ◮ ❚❤❡ ❧❡♥❣t❤ ♦❢ ❛♥ ✐♥t❡r✈❛❧ ✐s t❤❡ r✐❣❤t ❡♥❞♣♦✐♥t ♠✐♥✉s t❤❡

❧❡❢t ❡♥❞♣♦✐♥t✳

◮ ❚❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❛♥ ✐♥t❡r✈❛❧ ❡✈❡♥t E ✐s t❤❡ ❧❡♥❣t❤ ♦❢ E

❞✐✈✐❞❡❞ ❜② t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

◮ ❚❤❡ ✐♥t❡rs❡❝t✐♦♥ ♦❢ t✇♦ ✐♥t❡r✈❛❧s ✐s t❤❡ ✐♥t❡r✈❛❧ ❢♦r♠❡❞ ❜②

t❤❡✐r ♦✈❡r❧❛♣✳

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SLIDE 4

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡♠✐♥❞❡rs

❯s❡ ❝♦♥t✐♥✉♦✉s ♣r♦❜❛❜✐❧✐t② ✇❤❡♥ ♣✐❝❦✐♥❣ r❛♥❞♦♠ r❡❛❧ ♥✉♠❜❡rs✳

◮ ❙❛♠♣❧❡ s♣❛❝❡s ❛♥❞ ❡✈❡♥ts ❛r❡ ♠❛❞❡ ✉♣ ♦❢ ✐♥t❡r✈❛❧s✳ ◮ ❚❤❡ ❧❡♥❣t❤ ♦❢ ❛♥ ✐♥t❡r✈❛❧ ✐s t❤❡ r✐❣❤t ❡♥❞♣♦✐♥t ♠✐♥✉s t❤❡

❧❡❢t ❡♥❞♣♦✐♥t✳

◮ ❚❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❛♥ ✐♥t❡r✈❛❧ ❡✈❡♥t E ✐s t❤❡ ❧❡♥❣t❤ ♦❢ E

❞✐✈✐❞❡❞ ❜② t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

◮ ❚❤❡ ✐♥t❡rs❡❝t✐♦♥ ♦❢ t✇♦ ✐♥t❡r✈❛❧s ✐s t❤❡ ✐♥t❡r✈❛❧ ❢♦r♠❡❞ ❜②

t❤❡✐r ♦✈❡r❧❛♣✳

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SLIDE 5

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡✈✐❡✇

❈♦♥s✐❞❡r t❤❡ s❛♠♣❧❡ s♣❛❝❡ Ω = [✶✵,✶✼] ❛♥❞ ❡✈❡♥t ✭✐♥t❡r✈❛❧✮ F = [✶✸,✶✻]✿

◮ ❚❤❡ s❛♠♣❧❡ s♣❛❝❡ ❤❛s ❧❡♥❣t❤ ✼ −✵ = ✼. ◮ ❊✈❡♥t F ❤❛s ❧❡♥❣t❤ ✻−✸ = ✸. ◮ ❍❡♥❝❡ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ F ✐s

▲❡♥❣t❤ ♦❢ F ❚♦t❛❧ ❧❡♥❣t❤ = ✸ ✼. ◆♦t✐❝❡ t❤❛t F t❛❦❡s ✉♣ ✸✴✼t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

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SLIDE 6

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡✈✐❡✇

❈♦♥s✐❞❡r t❤❡ s❛♠♣❧❡ s♣❛❝❡ Ω = [✶✵,✶✼] ❛♥❞ ❡✈❡♥t ✭✐♥t❡r✈❛❧✮ F = [✶✸,✶✻]✿

◮ ❚❤❡ s❛♠♣❧❡ s♣❛❝❡ ❤❛s ❧❡♥❣t❤ ✼ −✵ = ✼. ◮ ❊✈❡♥t F ❤❛s ❧❡♥❣t❤ ✻−✸ = ✸. ◮ ❍❡♥❝❡ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ F ✐s

▲❡♥❣t❤ ♦❢ F ❚♦t❛❧ ❧❡♥❣t❤ = ✸ ✼. ◆♦t✐❝❡ t❤❛t F t❛❦❡s ✉♣ ✸✴✼t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

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SLIDE 7

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡✈✐❡✇

❈♦♥s✐❞❡r t❤❡ s❛♠♣❧❡ s♣❛❝❡ Ω = [✶✵,✶✼] ❛♥❞ ❡✈❡♥t ✭✐♥t❡r✈❛❧✮ F = [✶✸,✶✻]✿

◮ ❚❤❡ s❛♠♣❧❡ s♣❛❝❡ ❤❛s ❧❡♥❣t❤ ✶✼ −✶✵ = ✼. ◮ ❊✈❡♥t F ❤❛s ❧❡♥❣t❤ ✶✻−✶✸ = ✸. ◮ ❍❡♥❝❡ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ F ✐s

▲❡♥❣t❤ ♦❢ F ❚♦t❛❧ ❧❡♥❣t❤ = ✸ ✼. ◆♦t✐❝❡ t❤❛t F t❛❦❡s ✉♣ ✸✴✼t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

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SLIDE 8

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡✈✐❡✇

❈♦♥s✐❞❡r t❤❡ s❛♠♣❧❡ s♣❛❝❡ Ω = [✶✵,✶✼] ❛♥❞ ❡✈❡♥t ✭✐♥t❡r✈❛❧✮ F = [✶✸,✶✻]✿

◮ ❚❤❡ s❛♠♣❧❡ s♣❛❝❡ ❤❛s ❧❡♥❣t❤ ✶✼ −✶✵ = ✼. ◮ ❊✈❡♥t F ❤❛s ❧❡♥❣t❤ ✶✻−✶✸ = ✸. ◮ ❍❡♥❝❡ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ F ✐s

▲❡♥❣t❤ ♦❢ F ❚♦t❛❧ ❧❡♥❣t❤ = ✸ ✼. ◆♦t✐❝❡ t❤❛t F t❛❦❡s ✉♣ ✸✴✼t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

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SLIDE 9

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡✈✐❡✇

❈♦♥s✐❞❡r t❤❡ s❛♠♣❧❡ s♣❛❝❡ Ω = [✶✵,✶✼] ❛♥❞ ❡✈❡♥t ✭✐♥t❡r✈❛❧✮ F = [✶✸,✶✻]✿

◮ ❚❤❡ s❛♠♣❧❡ s♣❛❝❡ ❤❛s ❧❡♥❣t❤ ✶✼ −✶✵ = ✼. ◮ ❊✈❡♥t F ❤❛s ❧❡♥❣t❤ ✶✻−✶✸ = ✸. ◮ ❍❡♥❝❡ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ F ✐s

▲❡♥❣t❤ ♦❢ F ❚♦t❛❧ ❧❡♥❣t❤= ✸ ✼. ◆♦t✐❝❡ t❤❛t F t❛❦❡s ✉♣ ✸✴✼t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

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SLIDE 10

❈♦♥t✐♥✉♦✉s Pr♦❜❛❜✐❧✐t② ❘❡✈✐❡✇

❈♦♥s✐❞❡r t❤❡ s❛♠♣❧❡ s♣❛❝❡ Ω = [✶✵,✶✼] ❛♥❞ ❡✈❡♥t ✭✐♥t❡r✈❛❧✮ F = [✶✸,✶✻]✿

◮ ❚❤❡ s❛♠♣❧❡ s♣❛❝❡ ❤❛s ❧❡♥❣t❤ ✶✼ −✶✵ = ✼. ◮ ❊✈❡♥t F ❤❛s ❧❡♥❣t❤ ✶✻−✶✸ = ✸. ◮ ❍❡♥❝❡ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ F ✐s

▲❡♥❣t❤ ♦❢ F ❚♦t❛❧ ❧❡♥❣t❤ = ✸ ✼. ◆♦t✐❝❡ t❤❛t F t❛❦❡s ✉♣ ✸✴✼t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ t❤❡ s❛♠♣❧❡ s♣❛❝❡✳

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SLIDE 11

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s

▲❡t E ❛♥❞ F ❜❡ ❡✈❡♥ts ✐♥ ❛ s❛♠♣❧❡ s♣❛❝❡ Ω✳ ❚❤❡♥ t❤❡ ♣r♦❜❛❜✐❧✐t② ♦❢ ❡✈❡♥t F ❣✐✈❡♥ t❤❛t E ♦❝❝✉rr❡❞ ✐s P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E .

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SLIDE 12

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✭❉❡t❛✐❧s✮

▲❡t E ❛♥❞ F ❜❡ ❡✈❡♥ts ✐♥ ❛ s❛♠♣❧❡ s♣❛❝❡ Ω✳ ❲❡ ❤❛✈❡ s❡❡♥ t❤❛t P(F|E) = P(E F) P(E) . ■♥ t❡r♠s ♦❢ ❧❡♥❣t❤s✱ ✇❡ ❤❛✈❡ P(F|E) = ▲❡♥❣t❤ ♦❢ E F ❚♦t❛❧ ❧❡♥❣t❤ ▲❡♥❣t❤ ♦❢ E ❚♦t❛❧ ❧❡♥❣t❤ , ❛♥❞ t❤✐s s✐♠♣❧✐✜❡s t♦ t❤❡ ❢r❛❝t✐♦♥ P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E .

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SLIDE 13

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✶

▲❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✻]✱ ❛♥❞ F = [✶✷,✶✺]✳ ▲❡t ✉s ❝♦♠♣✉t❡ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

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SLIDE 14

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✶

▲❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✻]✱ ❛♥❞ F = [✶✷,✶✺]✳ ▲❡t ✉s ❝♦♠♣✉t❡ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

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SLIDE 15

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✶

▲❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✻]✱ ❛♥❞ F = [✶✷,✶✺]✳ ▲❡t ✉s ❝♦♠♣✉t❡ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

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SLIDE 16

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✶

▲❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✻]✱ ❛♥❞ F = [✶✷,✶✺]✳ ▲❡t ✉s ❝♦♠♣✉t❡ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

E ❛♥❞ F ♦✈❡r❧❛♣ ♦♥ [✶✷,✶✺], ✇❤✐❝❤ ❤❛s ❧❡♥❣t❤ ✶✺ −✶✷ = ✸✳

◮ ▲❡♥❣t❤ ♦❢ E ✐s ✶✻−✶✶ = ✺✳ ◮ ❍❡♥❝❡

P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✸ ✺. ◆♦t✐❝❡ t❤❛t E F t❛❦❡s ✉♣ ✸✴✺t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ E✳

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SLIDE 17

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✶

▲❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✻]✱ ❛♥❞ F = [✶✷,✶✺]✳ ▲❡t ✉s ❝♦♠♣✉t❡ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

E ❛♥❞ F ♦✈❡r❧❛♣ ♦♥ [✶✷,✶✺], ✇❤✐❝❤ ❤❛s ❧❡♥❣t❤ ✶✺ −✶✷ = ✸✳

◮ ▲❡♥❣t❤ ♦❢ E ✐s ✶✻−✶✶ = ✺✳ ◮ ❍❡♥❝❡

P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✸ ✺. ◆♦t✐❝❡ t❤❛t E F t❛❦❡s ✉♣ ✸✴✺t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ E✳

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SLIDE 18

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✶

▲❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✻]✱ ❛♥❞ F = [✶✷,✶✺]✳ ▲❡t ✉s ❝♦♠♣✉t❡ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

E ❛♥❞ F ♦✈❡r❧❛♣ ♦♥ [✶✷,✶✺], ✇❤✐❝❤ ❤❛s ❧❡♥❣t❤ ✶✺ −✶✷ = ✸✳

◮ ▲❡♥❣t❤ ♦❢ E ✐s ✶✻−✶✶ = ✺✳ ◮ ❍❡♥❝❡

P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✸ ✺. ◆♦t✐❝❡ t❤❛t E F t❛❦❡s ✉♣ ✸✴✺t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ E✳

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SLIDE 19

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✶

▲❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✻]✱ ❛♥❞ F = [✶✷,✶✺]✳ ▲❡t ✉s ❝♦♠♣✉t❡ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

E ❛♥❞ F ♦✈❡r❧❛♣ ♦♥ [✶✷,✶✺], ✇❤✐❝❤ ❤❛s ❧❡♥❣t❤ ✶✺ −✶✷ = ✸✳

◮ ▲❡♥❣t❤ ♦❢ E ✐s ✶✻−✶✶ = ✺✳ ◮ ❍❡♥❝❡

P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✸ ✺. ◆♦t✐❝❡ t❤❛t E F t❛❦❡s ✉♣ ✸✴✺t❤s ♦❢ t❤❡ t♦t❛❧ ❧❡♥❣t❤ ♦❢ E✳

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SLIDE 20

❄✭✾✳✶✮ ❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② Pr❛❝t✐❝❡ ✶

▲❡t Ω = [✷✹,✹✼]✱ E = [✷✾,✹✸]✱ ❛♥❞ F = [✸✹,✸✽]✳ ❈♦♠♣✉t❡ P(F|E)✳ ❍✐♥ts✿ ✶✳ ■❞❡♥t✐❢② t❤❡ ✐♥t❡rs❡❝t✐♦♥ ♦❢ [✷✾,✹✸] ❛♥❞ [✸✹,✸✽] ❛s ❛♥ ✐♥t❡r✈❛❧✳ ✷✳ ❲❤❛t ✐s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✐♥t❡rs❡❝t✐♦♥❄ ✸✳ ❲❤❛t ✐s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ❣✐✈❡♥ ❡✈❡♥t❄ ✹✳ ❆♥s✇❡r t❤❡ q✉❡st✐♦♥ ❜② ❞✐✈✐❞✐♥❣ t❤❡ ❛♣♣r♦♣r✐❛t❡ ❧❡♥❣t❤s✳

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SLIDE 21

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② Pr❛❝t✐❝❡ ✶

▲❡t Ω = [✷✹,✹✼]✱ E = [✷✾,✹✸]✱ ❛♥❞ F = [✸✹,✸✽]✳ ❈♦♠♣✉t❡ P(F|E)✳ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿ E ❛♥❞ F ♦✈❡r❧❛♣ ♦♥ [✸✹,✸✽], ✇❤✐❝❤ ❤❛s ❧❡♥❣t❤ ✸✽ −✸✹ = ✹✳ E ✐ts❡❧❢ ❤❛s ❧❡♥❣t❤ ✹✸ −✷✾ = ✶✹✳ ❍❡♥❝❡ P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✹ ✶✹.

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SLIDE 22

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✷

◆♦✇ ❧❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✺]✱ ❛♥❞ F = [✶✸,✶✻]✳ ❋✐♥❞ P(F|E)✳

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SLIDE 23

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✷

◆♦✇ ❧❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✺]✱ ❛♥❞ F = [✶✸,✶✻]✳ ❋✐♥❞ P(F|E)✳

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SLIDE 24

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✷

◆♦✇ ❧❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✺]✱ ❛♥❞ F = [✶✸,✶✻]✳ ❋✐♥❞ P(F|E)✳

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SLIDE 25

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✷

◆♦✇ ❧❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✺]✱ ❛♥❞ F = [✶✸,✶✻]✳ ❋✐♥❞ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

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SLIDE 26

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✷

◆♦✇ ❧❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✺]✱ ❛♥❞ F = [✶✸,✶✻]✳ ❋✐♥❞ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

E

  • F = [✶✸,✶✺], s♦ ✐ts ❧❡♥❣t❤ ✐s ✶✺−✶✸ = ✷.

◮ ▲❡♥❣t❤ ♦❢ E ✐s ✶✺−✶✶ = ✹✳ ◮ ❈♦♠♣✉t❡ P(F|E) ✉s✐♥❣ ❧❡♥❣t❤s✿

P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✷ ✹.

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SLIDE 27

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✷

◆♦✇ ❧❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✺]✱ ❛♥❞ F = [✶✸,✶✻]✳ ❋✐♥❞ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

E

  • F = [✶✸,✶✺], s♦ ✐ts ❧❡♥❣t❤ ✐s ✶✺−✶✸ = ✷.

◮ ▲❡♥❣t❤ ♦❢ E ✐s ✶✺−✶✶ = ✹✳ ◮ ❈♦♠♣✉t❡ P(F|E) ✉s✐♥❣ ❧❡♥❣t❤s✿

P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✷ ✹.

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SLIDE 28

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② ❢♦r ■♥t❡r✈❛❧s ✷

◆♦✇ ❧❡t Ω = [✶✵,✶✼]✱ E = [✶✶,✶✺]✱ ❛♥❞ F = [✶✸,✶✻]✳ ❋✐♥❞ P(F|E)✳

◮ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿

E

  • F = [✶✸,✶✺], s♦ ✐ts ❧❡♥❣t❤ ✐s ✶✺−✶✸ = ✷.

◮ ▲❡♥❣t❤ ♦❢ E ✐s ✶✺−✶✶ = ✹✳ ◮ ❈♦♠♣✉t❡ P(F|E) ✉s✐♥❣ ❧❡♥❣t❤s✿

P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✷ ✹.

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SLIDE 29

❄✭✾✳✷✮ ❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② Pr❛❝t✐❝❡ ✷

▲❡t Ω = [✹✼,✼✽]✱ E = [✺✶,✻✵]✱ ❛♥❞ F = [✺✹,✻✸]✳ ❈♦♠♣✉t❡ P(F|E)✳ ❍✐♥ts✿ ✶✳ ■❞❡♥t✐❢② t❤❡ ✐♥t❡rs❡❝t✐♦♥ ♦❢ [✺✶,✻✵] ❛♥❞ [✺✹,✻✸] ❛s ❛♥ ✐♥t❡r✈❛❧✳ ✷✳ ❲❤❛t ✐s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✐♥t❡rs❡❝t✐♦♥❄ ✸✳ ❲❤❛t ✐s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ❣✐✈❡♥ ❡✈❡♥t❄ ✹✳ ❆♥s✇❡r t❤❡ q✉❡st✐♦♥ ❜② ❞✐✈✐❞✐♥❣ t❤❡ ❛♣♣r♦♣r✐❛t❡ ❧❡♥❣t❤s✳

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SLIDE 30

❄✭✾✳✷✮ ❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② Pr❛❝t✐❝❡ ✷

▲❡t Ω = [✹✼,✼✽]✱ E = [✺✶,✻✵]✱ ❛♥❞ F = [✺✹,✻✸]✳ ❈♦♠♣✉t❡ P(F|E)✳ ❍✐♥ts✿ ✶✳ ■❞❡♥t✐❢② t❤❡ ✐♥t❡rs❡❝t✐♦♥ ♦❢ [✺✶,✻✵] ❛♥❞ [✺✹,✻✸] ❛s ❛♥ ✐♥t❡r✈❛❧✳ ✷✳ ❲❤❛t ✐s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ✐♥t❡rs❡❝t✐♦♥❄ ✸✳ ❲❤❛t ✐s t❤❡ ❧❡♥❣t❤ ♦❢ t❤❡ ❣✐✈❡♥ ❡✈❡♥t❄ ✹✳ ❆♥s✇❡r t❤❡ q✉❡st✐♦♥ ❜② ❞✐✈✐❞✐♥❣ t❤❡ ❛♣♣r♦♣r✐❛t❡ ❧❡♥❣t❤s✳

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SLIDE 31

❈♦♥❞✐t✐♦♥❛❧ Pr♦❜❛❜✐❧✐t② Pr❛❝t✐❝❡ ✷

▲❡t Ω = [✹✼,✼✽]✱ E = [✺✶,✻✵]✱ ❛♥❞ F = [✺✹,✻✸]✳ ❈♦♠♣✉t❡ P(F|E)✳ ❋✐♥❞ E F ❛♥❞ ✐ts ❧❡♥❣t❤✿ E ❛♥❞ F ♦✈❡r❧❛♣ ♦♥ [✺✹,✻✵], ✇❤✐❝❤ ❤❛s ❧❡♥❣t❤ ✻✵ −✺✹ = ✻✳ ❙✐♥❝❡ E ❤❛s ❧❡♥❣t❤ ✻✵−✺✶ = ✾✱ P(F|E) = ▲❡♥❣t❤ ♦❢ E F ▲❡♥❣t❤ ♦❢ E = ✻ ✾.