Consider the following R function

mysomething $=$ function$($n$)\{$

u $=$ runif$($n$,0,1)$

x $=0*$u

for$($k in $1$:n$)\{$

if$($u$[$k$]<1/2)\{$x$[$k$]=1\}$

else if$($u$[$k$]<3/4)\{$x$[$k$]=2\}$

else if$($u$[$k$]<7/8)\{$x$[$k$]=3\}$

else if$($u$[$k$]<15/16)\{$x$[$k$]=4\}$

else if$($u$[$k$]<31/32)\{$x$[$k$]=5\}$

else if$($u$[$k$]<=1)\{$x$[$k$]=6\}\}$

return$($x$)\}$

From what distribution does mysomething draw n samples from? Be as specific as possible.

To receive full credit, write down the set of outcomes and corresponding probabilities of this

distribution.

x $123456$

P$($X $=$ x$)1/21/41/81/161/321/32$