(Solved): A random variable \( \mathrm{X} \) is normally distributed with a mean of 81 and a variance of 81 , ...
A random variable \( \mathrm{X} \) is normally distributed with a mean of 81 and a variance of 81 , and a random variable \( Y \) is normally distributed with a mean of 180 and a variance of 324 . The random variables have a correlation coefficient equal to \( 0.4 \). Find the mean and variance of the random variable below. \[ W=8 X+5 Y \]