$Y = \frac { K A ^ { 3 } } { ( B + D ) ( C - D ) }$

Question

K is a constant

Find an expression to approximately determine the variance of Y, assuming $A , B , C ,$ and $D$ are probabilistically independent.

isnt the expression they have already given me the expression that determines the variance of Y

Answer 1

Your $Y$ is undefined when $C-D = 0$, and "blows up" as $C-D \to 0$. The variance won't exist if, e.g., $C-D$ has a density that approaches a nonzero constant at $0$. In order for it to exist you'll want to assume $C$ and $D$ are supported in disjoint intervals. Similarly for $B$ and $-D$.