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Probability : Density and Distribution Functions - Sketch

Assume that the proportion of commercial vehicles among users of the Humber Bridge varies randomly from day to day, with density {see attachment} over 0<x<1, where c is a constant. Show that c = 12, find the distribution function, and sketch the density and distribution functions over -1<x<2.
On what fraction of days is the proportion of commercial vehicles between 20% and 50%?

Verify that f(x) = -ln(x) for 0<x<1 is a density function and sketch it. Write A = (1/4,3/4) and B = (0,1/2). Use your density sketch to assess which is bigger, P(a) or P(A|B). Calculate both values and check your assessment.

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Solution to 3.11.

Since is a density function, by definition of a density function, we have

So,

i.e.,

i.e.,

Now we want to find the distribution function F(x). By the relation between ...

Solution Summary

Probability Density and Distribution Functions are investigated. The solution is detailed and well presented. The response received a rating of "5" from the student who originally posted the question.

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