Covariance properties

Probability Level 1

if X X is a standard normal random variable and Y = 3 X Y = 3X , what is Cov ( X , Y ) \text{Cov}(X, Y) ?


The answer is 3.

Lawrence Chiou by Lawrence Chiou , 28, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Standard normal variable is a special case of normal distribution. It has mean of 0 and standard deviation of 1. Knowing this: C o v ( X , Y ) = C o v ( X , 3 X ) = 3 ⋅ C o v ( X , X ) = 3 ⋅ V a r ( X ) = 3 ⋅ 1 2 = 3 Cov(X, Y) = Cov(X, 3X) = 3 \cdot Cov(X, X) = 3 \cdot Var(X) = 3 \cdot 1^2 = 3

2 Helpful 1 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...