The life (in months) of a certain electronic computer part has a probability density function defined by f(x) = 1/2e^(-x/2) for x in [0, infinity). Find the probability that a randomly selected component will last the following length of time. A.) Between 4 and 8 months B.) Find the cumulative distribution function for this random variable. C.) Use the answer from part B to find the probability that a randomly selected component will last at most 6 months.
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Step 1
Given the probability density function \( f(x) = \frac{1}{2}e^{-\frac{x}{2}} \) for \( x \in [0, \infty) \), we need to calculate the integral from 4 to 8: \[ P(4 \leq X \leq 8) = \int_{4}^{8} \frac{1}{2}e^{-\frac{x}{2}} dx \] \[ = \frac{1}{2} \int_{4}^{8} Show more…
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