The chance of an IRS audit for a tax return with over $$25,000$ in income is about $2\%$ per year. We are interested in the expected number of audits a person with that income has in a $5-$year period. Assume each year is independent.

Part $($a$)$

In words, define the Random Variable $x.$

the number of audits the IRS does each year

the yearly income of a person

the number of audits a person who has an income over $$25,000$ receives in a $5-$year period

the number of audits the IRS does every $5$ years for a person who has an income over $$25,000$

Part $($b$)$

List the values that $x$ may take on$.$

$x=1,2,3,$dots

$x=1,2,3,$dots,$98,99,100$

$x=0,1,2,$dots,$4,5$

$x=1,2,3,$dots,$4,5$

Part $($c$)$

Give the distribution of $x$