Problem
X ~ N(0, 1)
Let W be independent of X with P(W = 1) = P(W = −1) = 1
Y = WX
It is found that Y ~ N(0,1).
Are X and Y jointly normal?
Question
Answer key said: "Clearly X and Y are not independent but uncorrelated. This implies that (X, Y ) are not jointly normal"
Why does NOT independent & uncorrelated imply NOT jointly normal? What is the definition of jointly normal?
$\endgroup$ 2 Reset to default
