1. Look at the shape of the binomial distribution for various combinations of n and p. Speci?cally, let n = 5 and try p = 0.2, 0.5, and 0.8. Repeat the same for other values of n. Can you say something about how the skewness of the distribution is affected by p and n?
2. Try various values of s and p on the negative binomial distribution template and answer this question: How is the skewness of the negative binomial distribution affected by s and p values?
3. An MBA graduate keeps interviewing for jobs, one by one, and will stop interviewing on receiving an offer. In each interview he has an independent proba- bility 0.2166 of getting the job.
a. What is the expected number of interviews? What is the variance?
b. If there is enough time for only six interviews, how con?dent can he be of getting a job within the available time?
c. If he wants to be at least 95% con?dent of getting a job, how many inter- views should he be prepared for?
d. Suppose there is enough time for at most six interviews. For what mini- mum value of p can he have 95% con?dence of getting a job within the available time?
e. In order to answer (d ) more thoroughly, tabulate the con?dence level for p values ranging from 0.1 to 0.5 in steps of 0.05.