Random Variableshard
0:00.0

Suppose XX and YY are independent random variables where E[X]=μXE[X] = \mu_X, Var(X)=σX2Var(X) = \sigma^2_X, E[Y]=μYE[Y] = \mu_Y, and Var(Y)=σY2Var(Y) = \sigma^2_Y. If we define Z=X/YZ = X/Y where Y>0Y > 0, under what condition is the variance of ZZ approximately equal to μX2μY2(σX2μX2+σY2μY2)\frac{\mu_X^2}{\mu_Y^2} (\frac{\sigma_X^2}{\mu_X^2} + \frac{\sigma_Y^2}{\mu_Y^2})?