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The CPU of a personal computer has a lifetime that is exponentially distributed with a mean lifetime of six years. a) What is the probability that the CPU fails within three years?

Respuesta :

Answer: Our required probability is 0.39.

Step-by-step explanation:

Since we have given that

X be the exponentially distributed with mean life = 6 years

So, E[x]=6

[tex]\dfrac{1}{\lambda}=6\\\\\lambda=\dfrac{1}{6}[/tex]

So, our cumulative distribution function would be

[tex]F(x)=1-e^{-\lambda x}[/tex]

We need to find the probability that the CPU fails within 3 years.

[tex]P(X<3)=F(3)=1-e^{-\frac{1}{6}\times 3}\\\\=1-e^{-\frac{1}{2}}\\\\\approx 0.39[/tex]

Hence, our required probability is 0.39.

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