0 Question 1 v Both the Geometric and Binomial distributions are used when there are only two possible outcomes in a trial (success and failure}, but: '33:? in the binomial, the probability of success must be the same for each trial, but in the geometric it can be different. '33:? in the binomial, the trials must be independent, but in the geometric they can be dependent. '3' in the geometric, you count the number of successes in a fixed number of trials, whereas in the binomial you count the number of trials until the first success. '3' in the binomial, you count the number of successes in a fixed number of trials, whereas in the geometric you count the number of trials until the first success. 0 Question 2 'r The defining characteristic of a Geometric Distribution is that in a given trial there are only two possible outcomes {"success" and "failure"} and: '33::3' X counts the expected number of successes in n trials '13:} X counts the number of successes over an interval of time or space '3' X counts the number of trials until the first success '3' X counts the number of successes in n trials 0 Question 3 Given a Geometric Distribution, match each symbol to the correct quantity. C d E + number of trials until first success . probability of failure in a single trial . number of failures before first success + does not apply to the Geometric Distribution + probability of success in a single trial 0 Question 4 v Suppose that during a pandemic, 8 percent of people in a region test positive for a virus. You repeatedly test people from this region until you find someone who tests positive, and you are interested in the probability that the first positive test will be the 19th person tested. Because we keep testing until the first positive test, this situation can be modeled using a Geometric Distribution with: a Success = '33:? a person tests positive '33:? a person gets tested '33:? a person does not test positive '33:? 19 people test positive