Two independent random variable $X$ and $Y$ have the distribution $\mathrm{N}\left( 2\mu ,{{\sigma }

Question

Two independent random variable $X$ and $Y$ have the distribution $\mathrm{N}\left( 2\mu ,{{\sigma }^{2}} \right)$ and $\mathrm{N}\left( 3\mu ,3{{\sigma }^{2}} \right)$ respectively. Given that $\mathrm{P}\left( X Write down the mean and the variance of $Y-X$. Hence find $\mathrm{P}\left( \left| Y-X-\mu \right|>4{{\sigma }^{2}} \right)$ in terms of $k$.

Accepted Answer

(i) Shown (ii) $2(1-k)$

2008 VJC BT P2 Q14

2008 VJC BT P2 Q14

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