Question

1. A statistics professor posted 10 review problems on probability distributions: 4 problems were on discrete distributions and 6 on continuous distributions. He then announced to his students that he will randomly select 3 problems out of those posted problems and use them on the midterm exam. Let X be the number of posted problems the professor ends up using on the exam that deal with discrete distributions. a. How many different selections of 3 problems are possible? b. Find P(X = 0)=P(all three problems are on continuous distributions) c. Find P(X = 1)=P(one discrete and two continuous distributions are selected) d. Find P(X = 2)=P(two discrete and one continuous distributions are selected) e. Find P(X = 3)=P(all three selected problems are on discrete distribution) f. Find the mean value of X.

Answer 1

solution: Jo 2 6 continious 4 discrete (B) (A) X^ Hyber geometric 10! a) Total possible selechon = (10) = 21 - (3) 3!:(10-3) ! - 120 b) piko) = (99) # (3) 9 Plx= 1) = (1) (3) - | e) = (0)49) Pl=> = 13)(8) + EX MIA) 9 - 1x) = m an (A) P+B 1.2 3x 4 4+6 1-2 |