Exercice 32                               ∞                                     αdt    (a) On cherche α tel que       (1+t...
Exercice 32 (suite..)    (b) On calcule l’espérance mathématique E(t)                   ∞                  ∞              ...
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Ch20 32

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Ch20 32

  1. 1. Exercice 32 ∞ αdt (a) On cherche α tel que (1+t)4 =1 0 Comme : ∞ ∞ αdt α(1 + t)−3 α = = (1 + t)4 −3 −3(1 + t)3 0 0 α α =0− = −3(1 + 0)3 3 Ainsi : α =1→α=3 3
  2. 2. Exercice 32 (suite..) (b) On calcule l’espérance mathématique E(t) ∞ ∞ ∞ 3 t dt t · N(t)dt = t· dt = 3 (1 + t)4 0 (1 + t)4 −∞ 0 En intégrant par parties, on obtient : ∞ −3t − 1 1 1 E(t) = =0− − = 2(1 + t)3 0 2 2 (c) +∞ 3 P(x > 2) = dt (1 + t)4 2 ∞ 1 1 − =0− − 0, 037 (1 + t)3 2 33

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