Question: The time X (min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution with A

The timeX(min) for a lab assistant to prepare the equipment for a certain experiment is believed to have a uniform distribution withA= 25andB= 35.(a) Determine the pdf ofX.

f(x) =

x0otherwise

Sketch the corresponding density curve.

(b) What is the probability that preparation time exceeds31min?

(c) What is the probability that preparation time is within1min of the mean time? [Hint: Identifyfrom the graph off(x).]

(d) For anyasuch that 25 <a<a+1< 35, what is the probability that preparation time is betweenaanda+1min?

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