# Random Variables

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).

https://brainmass.com/statistics/probability/standard-normal-random-variables-11954

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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).

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