Covariance and Correlation of Linear Combinations of the Standard Normal Distribution
The standard normal distribution,has mean 0 and variance = standard deviation = 1. If we have two distributionsandthen the covariance between them isIfandare independent thenso If howeverandare linear combinations of independently distributed standard normal distributionssayandthenandare not independent, even thoughandare. We can find theand the correlation betweenand
The formula for the correlation betweenandis
Then the correlation betweenandis
We can follow the same procedure for any linear combination of standard normal distributions.