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Sagot :
Given: 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 a mean of 12 years.
Required: To determine the probability of failure in the first 8 years.
Explanation: Acording to the question,
[tex]\begin{gathered} \frac{1}{\lambda}=12 \\ \lambda=\frac{1}{12} \end{gathered}[/tex]As we know,
The cumulative distributive function will be:
[tex]1-e^{-\lambda x}[/tex]Hence, In the first 8 years the probability of failure is
[tex]\begin{gathered} P(X<8)=1-e^{-\frac{8}{12}} \\ =1-0.5134 \\ =0.4865 \end{gathered}[/tex]Final Answer: The probability of failure in the first 8 years is 0.4865.
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