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- Exercice 2:
- Question 1: MTBF = 392 donc lambda = 1 / 392 = 0.00255
- Question 2: F(365) = P(T <= 365) = 1 - e(-0.00255*365) = 0.61
- Question 3:
- 3 années = 3 * 365 = 1095
- R(1095) = P(T > 1095) = e(-0.00255*1095) = 0.06
- Question 4:
- P(T > n) >= 0.95
- <=> e(-0.00255*n) >= 0.95
- <=> -0.00255*n >= ln(0.95)
- <=> n <= ln(0.95)/(-0.00255)
- <=> n <= 20.11 soit n <= 20
- Question 5:
- a) F(365)^6 = (1 - e(-0.00255*365))^6 = 0.05
- b) 1 - F(365)^6 = 1 - 0.05 = 0.95
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