CSIR UGC NET June 2019 Part B Question 53

Question

Suppose $(X, Y)$ follows bivariate normal distribution with means $\mu_{1}, \mu_{2}$, standard deviations $\sigma_{1}, \sigma_{2}$ and correlation coefficient $\rho$, where all the parameters are unknown. Then testing $H_{0}: \sigma_{1}=\sigma_{2}$ is equivalent to testing the independence of

1. $X$ and $\bar{Y}$

2. $X$ and $X-Y$

3. $X+Y$ and $\underline{Y}$

4. $X+Y$ and $X-Y$