Question

Please state which of the following random variables are binomial, geometric, negative binomial, or hypergeometric a. Let # of lines in 100 lines of someone's computer program that have a bug. Assume each line of code is independently buggy of every other line and that the probability of a having a bug in a line of code is the same for each line. b. Let T the shot of tequila that you drink that makes you throw up. Assume the probability of throwing up on any shot is independent (impractical assumption, but let's just say it is so) of any other and P(throwing up) 1/3 (also impractical assumption). If we randomly sample 3 quizzes from the 40 class quizzes and 10 of those students got As on their quizzes, then let X-# of quizzes we sample that are As. c. d. The # parking spot you check out when you finally find an empty spot. Assume Let P each parking space is empty with a constant probability and that each spot is independently empty of every other. # of weeks where you average a good amount of sleep out of the 4 weeks in a Let W month. Assume your sleep in a given week is independent of every other week. Also assume P(successfully get a good average amount of sleep)-.2 e. Let S-Sample # at an ice cream store that you eat when you find the 3rd flavor that you like enough to buy (you're ambitiously going for a 3-scoop cone!). Assume your chance o liking any flavor is independent of every other flavor and assume P(liking a flavor) 1/5 f. # black socks if you randomly choose 2 socks from a drawer with 4 white socks. Let M greys socks, and 4 black socks. g.

Answer 1

A) binomial distribution since number of trials n = 100 is finite, probability of having a bug is constant and there are two outcomes of having a bug and not having a bug . Observation are independent.

B) Binomial distribution . ( Explanation same as above)

C) Hypergeometric distribution ( suppose there are N objects out of which G are termed as Success and now you draw a sample of n without replacement from N what is probability of g success in n ) N= 40, n= 3, G = 10. If sampling done with replacement it will be binomial.

D) geometric distribution ( occurrence of first success after series of failures)

E) Binomial distribution

F) Negative Binomial Distribution( there are X+ R trials, where X is number of failures and R is number of Success and last trial is success.) R =3 X= S-3

G) Hepergeometric distribution N=10 G= 4 n=2 ( if sampling is done without replacement)