The life (in hours) of a computer processing unit (CPU) is modeled as a weibull random variable with β=3 and α=901 hours. What is the probability that the CPU fails before 458 hours?
To find the probability that the CPU fails before 458 hours, we can use the cumulative distribution function (CDF) of the Weibull distribution.
The CDF of a Weibull distribution with parameters β and α is given by:
F(t) = 1 - e^(-(t/α)^β)
In this case, β = 3 and α = 901.
Substituting the values into the formula, we get:
F(t) = 1 - e^(-(t/901)^3)
To find the probability that the CPU fails before 458 hours, we need to evaluate the CDF at that point:
F(458) = 1 - e^(-((458/901)^3))
Calculating this value gives us the probability that the CPU fails before 458 hours.