QUESTION 3 The time (in hours) to failure of a component is exponential distributed with mean 40. In a manufacturing process, the machine involved uses one of these components continuously until it fails. a) Find the probability that a component will fail during a 12 to 18 hours shift. (2 marks) b) A component has not failed for 30 hours. Find the probability that this component lasts for at least another 30 hours. (3 marks)
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Given that the time to failure of a component is exponentially distributed with mean 40, the probability density function is \( f(x) = \frac{1}{40} e^{-\frac{x}{40}} \) for \( x > 0 \). To find the probability that the component will fail during a 12 to 18 hour Show more…
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The time (in hours) to failure of a component is exponential distributed with mean 40. In a manufacturing process, the machine involved uses one of these components continuously until it fails. a) Find the probability that a component will fail during a 12 to 18 hours shift. b) A component has not failed for 30 hours. Find the probability that this component lasts for at least another 30 hours.
Anas V.
The time (in hours) to failure of component is exponential distributed with mcan 40_ manufacturing process, the machine involved uses one of these components continuously until it fails Find the probability that component will fail during a 12 to 18 hours shift: 6) A component has not failed for 30 hours Find the probability that this component lasts for at least another 30 hours_
Ana Carolina D.
The lifetime (in hours) $Y$ of an electronic component is a random variable with density function given by $$f(y)=\left\{\begin{array}{ll} \frac{1}{100} e^{-y / 100}, & y>0 \\ 0, & \text { elsewhere } \end{array}\right.$$ Three of these components operate independently in a piece of equipment. The equipment fails if at least two of the components fail. Find the probability that the equipment will operate for at least 200 hours without failure.
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