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Dewar
@Dewar
May 2019
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Bonjour ! J'ai un exercice à faire sur la loi exponentielle et je galère. Merci pour votre aide ! Le voici :
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scoladan
Verified answer
Bonjour,
X loi exponentielle de paramètre 0,1
1) p(X≥15)
= 1 - p(X<15)
= 1 - e^(0,1x15)
= 1 - 0,7769
= 0,2231 à 10⁻⁴ près.
2) p(5<X<25)
= p(X<25) - p(X<5)
= 0,9179 - 0,3935
= 0,5244
3) p(X>30) sachant que X>15
= p(15>X>30)/p(X>15) (intersection/condition)
= (p(X≤30 - p(X≤15))/(1 - p(X≤15))
= 0,1733/0,7769
= 0,2230
2 votes
Thanks 1
Dewar
Merci beaucoup !
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Verified answer
Bonjour,X loi exponentielle de paramètre 0,1
1) p(X≥15)
= 1 - p(X<15)
= 1 - e^(0,1x15)
= 1 - 0,7769
= 0,2231 à 10⁻⁴ près.
2) p(5<X<25)
= p(X<25) - p(X<5)
= 0,9179 - 0,3935
= 0,5244
3) p(X>30) sachant que X>15
= p(15>X>30)/p(X>15) (intersection/condition)
= (p(X≤30 - p(X≤15))/(1 - p(X≤15))
= 0,1733/0,7769
= 0,2230