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GATE2018-1-26

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Let $X_1, \: X_2$ be two independent normal random variables with means $\mu_1, \: \ \mu_2$ and standard deviations $\sigma_1, \: \sigma_2$, respectively. Consider $Y=X_1-X_2; \: \mu_1 = \mu_2 =1, \: \sigma_1=1, \: \sigma_2=2$. Then, 

  1. $Y$ is normally distributed with mean $0$ and variance $1$
  2. $Y$ is normally distributed with mean $0$ and variance $5$
  3. $Y$ has mean $0$ and variance $5$, but is NOT normally distributed
  4. $Y$ has mean $0$ and variance $1$, but is NOT normally distributed
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