Explore BrainMass

Explore BrainMass

    Random Variables

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

    Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2.

    a) Find the joint density of Y1 and Y2
    b) Find the marginal density of Y1 and Y2 (The distribution of Y2 is known as the Cauchy distribution).

    © BrainMass Inc. brainmass.com March 4, 2021, 5:48 pm ad1c9bdddf
    https://brainmass.com/statistics/probability/standard-normal-random-variables-11954

    Solution Preview

    See attachment

    Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2.

    a) Find the joint density of ...

    Solution Summary

    Let X1 and X2 be two independent standard normal random variables. Let Y1 = X1+X2 and Y2=X1/X2.

    a) Find the joint density of Y1 and Y2
    b) Find the marginal density of Y1 and Y2 (The distribution of Y2 is known as the Cauchy distribution).

    $2.49

    ADVERTISEMENT