Explore BrainMass
Share

Explore BrainMass

    Transformation of Variables in Probability Distribution

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

    I've struggled for 3 days to come up with something approaching a relevant answer but am now desperate.

    Could you solve Q3, both a) and b) parts from the Exercise Sheet attached?

    Happy to pay 2 credits for both answers.

    Thank you very much.

    3. The random variable X has an exponential distribution with mean µ. Let Y = e
    −X/µ
    .
    (a) Use the method of transformations to find the probability density function of
    Y . [ 4 marks ]
    (b) Use the method of distribution functions to find the cumulative distribution
    function of Y .

    © BrainMass Inc. brainmass.com May 20, 2020, 11:50 pm ad1c9bdddf
    https://brainmass.com/math/probability/transformation-variables-probability-distribution-593874

    Attachments

    Solution Preview

    Explanations:

    Here is a somewhat modified version of your presentation for the method of transformations.
    I like it done in this way because I think it makes all the details transparent.

    First, we write down the exponential distribution:

    dP=1/μ e^(-X/μ) dX. X∈[0,∞) (1)

    It may be that you are more used to start from the PDF

    p(x)=dP(x)/dx=1/μ e^(-X/μ), (2)

    however it is often ...

    Solution Summary

    This solution explains in small details how to transform a probability distribution from one random variable to another

    $2.19

    ADVERTISEMENT