Question

On a recent trip to the SC DMV, I asked an employee to estimate what percentage of SC drivers arrive to renew their driver’s license with one that is currently expired. She responded that about 30 percent of all such renewals were of this type.

(a) Suppose you observe Y , the number of SC DMV customers seeking renewal to find the first one with an expired license. What is the distribution of Y? Plot the pmf and cdf of Y side by side (like in the notes). (Hint: You can just generate the Y from 1 to 20)

(b) Let W denote the number of SC DMV customers seeking renewal to find the 3rd one with an expired license. What is the distribution of W? Plot the pmf and cdf of W side by side (like in the notes).

(c) Obviously, in parts (a) and (b), you are assuming that Bernoulli trial assumptions hold. State what these are in this application (e.g., think of each customer seeking renewal as a “trial.”)

(d) In parts (a) and (b), find the probability that • among the first 6 customers seeking renewal, none have expired licenses. (Hint: use pgeom(y-1, p)) • you have to observe 10 or more customers seeking renewal to find the 3rd one with an expired license. (Hint: use pnbinom(w-r, r, p))

please include the R code

thanks

Answer 1