Suppose that the waiting time for a particular doctor is distributed as a unifor

Question

Suppose that the waiting time for a particular doctor is distributed as a uniform continuous distribution from zero minutes to twenty minutes.

What is c, the beginning of the interval where the probability density function, pdf, is non-zero?

What is d, the end of the interval where the pdf is non-zero?

What is the uniform height of the pdf? 1/______

What is the slope of the continuous distribution function, cdf, in the interval (c, d)? 1/

What is the MAXIMUM value of the cdf?

What is the expected waiting time?

What is the standard deviation of the waiting time?

What is the total area under the PDF?

Explanation / Answer

c = 0

d = 20

pdf = 1/(d-c) = 1/20

cdf = (x - c)/(d-c) c<x<d

slope of cdf = 1 /(d -c) = 1/20

maimum value of cdf = 1

expected waiting time = (d+c)/2 = 10 min

sd of waiting time = sqrt(1/12)*(d-c) = 20*sqrt(1/12) = 5.77350269

total area under pdf =1

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