Question

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

Answer 1

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:

⇒ $P(X$

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

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

                    $=1-0.6807$

                    $=0.3193$