# A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed

A system has two components: A and B. The operating times until failure of the two components are independent and exponentially distributed random variables with parameter 2 for component A, and parameter 3 for component B. The system fails at the first component failure.
(a) – Read section 1.5.2 in the textbook.
(b) – What is the mean time to failure for component A and for component B

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1. MichaelMet

$$E(x) = \frac{1}{2}$$ — Component A

$$E(x) = \frac{1}{3}$$ — Component B

Step-by-step explanation:

Given

Distribution = Exponential

$$\lambda = 2$$ — Component A

$$\lambda = 3$$ — Component B

Solving (a): The mean time of A

The mean of an exponential distribution is:

$$E(x) = \frac{1}{\lambda}$$

We have:

$$\lambda = 2$$ — Component A

$$E(x) = \frac{1}{2}$$

Solving (b): The mean time of B

The mean of an exponential distribution is:

$$E(x) = \frac{1}{\lambda}$$

We have:

$$\lambda = 3$$ — Component B

$$E(x) = \frac{1}{3}$$