# Statistically Independent Random Variables

Two statistically random variables, X and Y, have variances of 9 and 25 respectively. Two new random variables are defined by

U=3X+4Y

V=5X-2Y

A) Find the variances of U and V.

B) Find the correlation coefficient of U and V.

https://brainmass.com/statistics/random-variables/statistically-independent-random-variables-194460

#### Solution Preview

Two statistically random variables, X and Y, have variances of 9 and 25 respectively. Two new random variables are defined by

U=3X+4Y

V=5X-2Y

A)Find the variances of U and V.

We assume that X and Y are independent. Then

Var(U)=Var(3X+4Y)

...

#### Solution Summary

This solution solves the provided questions and shows all calculations to aid you in understanding each answer.

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