Let $$ be a random variable whose density is given by $()=\{0,>0,<=0,$ where $>0$

is a fixed parameter.

Part $($a$)$

Create R function likely$($theta$,$x$)$ which, for a given value of parameter theta and a given vector x $($which represents a sample from the population $$

$),$ returns the corresponding value of the likelihood function of parameter $$ of population $$

$,$ based on the sample x$.$

Note that since $()=0$

for $<=0$

$,$ we can assume that all the entries of the sample are positive. So$,$ think of R variable x as a vector

$(1,2,...,)$with $>0,$ for all $$ in $\{1,2,...,\}.$

In other words, you don't need to worry about how to handle situation in which $<=0$

for some $$ in $\{1,2,....,\}$

$($although in that case the likelihood equals $0,$ so it's trivial$).$

Your function likely$()$ should be flexible allowing vector x to be of any length.

Hint: After figuring out the mathematical formula for the likelihood function $($;$)$

$,$ your R function likely$()$ should have one or two lines of code. No loops, nor if$-$else statments, please! Loops are okay only when you cannot vectorize.