$7.$ Suppose that X is an exponential random variable with rate $\backslash$lambda $=10$ and we know how

to generate X$.$

$($a$)$ Explain how you would generate Y whose distribution follows an Erlang$($k$,\backslash$lambda $)$

where k $=3$ and $\backslash$lambda $=10.($Hint: What is the relationship between Erlang$($k$,\backslash$lambda $)$

and Exp$(\backslash$lambda $)?)$

$($b$)$ To generate five values of Y $,$ how many PRNs do we need when you use your

random$-$variate generator?