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svetoff [14.1K]
3 years ago
9

Many electronics follow a failure rate described by an exponential probability density function (PDF). Solar panels are advertis

ed to last 20 years or longer, but panels made in China are failing at a higher rate. The time-to-failure of this device is usually exponentially distributed with mean 13 years. What is the probability of failure in the first 5 years
Mathematics
1 answer:
katovenus [111]3 years ago
3 0

Answer:

The right answer is "0.3193".

Step-by-step explanation:

According to the question,

Mean,

\frac{1}{\lambda}  = 13

\lambda = \frac{1}{13}

As we know,

The cumulative distributive function will be:

⇒ 1-e^{-\lambda x}

hence,

In the first 5 years, the probability of failure will be:

⇒ P(X

                    =1-e^{-(\frac{1}{13} )\times 5}

                    =1-e^(-\frac{5}{13})

                    =1-0.6807

                    =0.3193

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