easy Probability

Correlation Shift I

A release-checked easy problem for training Covariance/Correlation.

Question

Let $X$ and $Y$ be random variables with $\corr{X}{Y} = \rho$. Define $U = aX + b$ and $V = cY + d$, where $a,b,c,$ and $d$ are all constants. Find $\corr{U}{V}$ when $a = b = 2, c = d = 3,$ and $\rho = 0.25$.

Practice focus

This Probability problem is tagged Covariance/Correlation. State the random variables and conditioning information explicitly, then check the result against boundary cases before opening hints or a solution.