Question

2. The lifetime Y (in hours) of an electronic component is a random variable with density function given by f(y) = { e^(-y/100) / 100, 0 <= y < infinity; 0, elsewhere. Three of these components operate independently in a piece of equipment. The equipment fails if at least two components fail. Let X be the number of components that lasts more than 200 hours. (a) What is the density function of Y. (b) Find the probability that an electronic component lasts more than 200 hours. (c) What is the probability distribution of X. (d) Find the probability that the equipment will operate for at least 200 hours without failure.

Uploaded: 2021-10-09T01:03:03-08:00
Duration: 4 min 55 s
Channel: David Nguyen

          2. The lifetime Y (in hours) of an electronic component is a random variable with density function given by f(y) = { e^(-y/100) / 100, 0 <= y < infinity; 0, elsewhere. Three of these components operate independently in a piece of equipment. The equipment fails if at least two components fail. Let X be the number of components that lasts more than 200 hours. (a) What is the density function of Y. (b) Find the probability that an electronic component lasts more than 200 hours. (c) What is the probability distribution of X. (d) Find the probability that the equipment will operate for at least 200 hours without failure.

2. The lifetime Y (in hours) of an electronic component is a random variable with density function given by f(y) = e^(-y/100) / 100, 0 <= y < infinity; 0, elsewhere. Three of these components operate independently in a piece of equipment. The equipment fails if at least two components fail. Let X be the number of components that lasts more than 200 hours. (a) What is the density function of Y. (b) Find the probability that an electronic component lasts more than 200 hours. (c) What is the probability distribution of X. (d) Find the probability that the equipment will operate for at least 200 hours without failure.

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Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Solved by Expert David Nguyen

10/09/2021

Step 1

The density function of Y is given by f(y) = 1/100 for 0 < y < c and 0 elsewhere. This means that the probability that a component lasts for a certain amount of time is uniformly distributed between 0 and c hours. Show more…

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The lifetime Y (in hours) of an electronic component is a random variable with density function given by f(y) = { e^(-y/100)/100, 0 <= y < infinity; 0, elsewhere. Three of these components operate independently in a piece of equipment. The equipment fails if at least two components fail. Let X be the number of components that lasts more than 200 hours. (a) What is the density function of Y. (b) Find the probability that an electronic component lasts more than 200 hours. (c) What is the probability distribution of X. (d) Find the probability that the equipment will operate for at least 200 hours without failure.