The number of errors, X$,$ per $100$ lines of software code has the fol$-$

lowing probability mass function:

x $23456$

p$($x$)0\mathrm{.}010\mathrm{.}250\mathrm{.}400\mathrm{.}300\mathrm{.}04$

$($a$)$ Verify that p$($x$)$ is a valid probability mass function.

$($b$)$ Calculate the expected number of errors per a $100-$lines page of

software code.

$($c$)$ Calculate the standard deviation of the number of errors per a

$100-$lines page of software code.

$($d$)$ Suppose it costs the company $$10($in developer$$s time$)$ to debug

each error. Calculate the expected cost to debug $100$ lines of

software code.