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

lowing probability mass function:

$($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.