Question $2.$ Let $\backslash$xi $=(\backslash$xi $1,\backslash$xi $2)$ be a two dimensional random vector, where the random variables $\backslash$xi $1$ and $\backslash$xi $2$ take values from the sets Z$1=\{1,2,..,10\}$ and Z$2=\{1,2,3,4,5\},$ respectively.

Also, let pij $=$ P$\{\backslash$xi $1=$ i$,\backslash$xi $2=$ j$\},$ where i in Z$1$ and j in Z$2.$ This joint probability mass

function is provided below:

pij $=$

$$

$$

$$

$0\mathrm{.}010$ if i in $\{1,2,7,8\}$ and $1<=$ j $<=5$ or i $=6$ and $3<=$ j $<=5$

$0\mathrm{.}040$ if i $=3$ and $1<=$ j $<=5$

$0\mathrm{.}002$ if i $=4$ and $1<=$ j $<=5$

$0\mathrm{.}050$ if i $=5$ and j in $\{1,2\}$

$0\mathrm{.}020$ if i $=5$ and j in $\{3,4\}$

$0\mathrm{.}160$ if i $=5$ and j $=5$

$0\mathrm{.}030$ if i $=6$ and j in $\{1,2\}$ or i $=9$ and $1<=$ j $<=4$

$0\mathrm{.}000$ if i $=9$ and j $=5$

$0\mathrm{.}016$ if i $=10$ and $1<=$ j $<=5$

Based on the above joint probability distribution, calculate the p$-$level efficient points for

p $=0\mathrm{.}4.$