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The radius of a yeast cell varies uniformly between ? − ? ?m. What is the...

The radius of a yeast cell varies uniformly between ? − ? ?m. What is the expected value of its surface area? If the O2 consumption rate (in µ?ol/ℎ) is calculated to be roughly equal to ??% of the square of the surface area, what is the expected value of O2 consumption for a single yeast cell in a day? Assume that a yeast cell can be modeled as a sphere.

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Answer #1

Given the radius of a yeast cell varies uniformly between ? − ? ?m. So the PDF of radius is

The surface area is . The expected value of is

Given  the O2 consumption rate (in µ?ol/ℎ) is calculated to be roughly equal to ??% of the square of the surface area, the expected value of O2 consumption for a single yeast cell in a day is

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