Explore BrainMass

Explore BrainMass

    Probability : Density and Distribution Functions - Sketch

    Not what you're looking for? Search our solutions OR ask your own Custom question.

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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.

    *Please see attachment for complete question

    © BrainMass Inc. brainmass.com March 4, 2021, 6:13 pm ad1c9bdddf
    https://brainmass.com/math/probability/probability-density-distribution-functions-sketch-35596

    Attachments

    Solution Preview

    Please see the attached file for the complete solution.
    Thanks for using BrainMass.

    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.

    $2.49

    ADVERTISEMENT