bac-s-maths 2020 Q4

bac-s-maths · France · polynesie 1 marks Exponential Distribution
The operating duration, expressed in years, of a motor until the first failure occurs is modelled by a random variable following an exponential distribution with parameter $\lambda$ where $\lambda$ is a strictly positive real number. The probability that the motor operates without failure for more than 3 years is equal to: Answer A: $e ^ { - 3 \lambda } \quad$ Answer B: $1 - e ^ { - 3 \lambda } \quad$ Answer C: $e ^ { 3 \lambda } - 1 \quad$ Answer D: $e ^ { 3 \lambda }$
A: $e^{-3\lambda}$
The operating duration, expressed in years, of a motor until the first failure occurs is modelled by a random variable following an exponential distribution with parameter $\lambda$ where $\lambda$ is a strictly positive real number.\\
The probability that the motor operates without failure for more than 3 years is equal to:\\
Answer A: $e ^ { - 3 \lambda } \quad$ Answer B: $1 - e ^ { - 3 \lambda } \quad$ Answer C: $e ^ { 3 \lambda } - 1 \quad$ Answer D: $e ^ { 3 \lambda }$