Chapter 6.3, Problem 110E

(a)

To determine

To find: whether of the following scenarios explain a geometric setting yes or not, If yes than define an appropriate geometric random variable.

Answer to Problem 110E

No geometric distribution

Explanation of Solution

A random variable has a geometric distribution when the variable contain two possible results, every draw is independent of the previous ones, The variables computes the number of draws required until the first success. Every draw has the same probability of success.

No geometric distribution, the reason is that every draw is not independent of the previous ones, although there is no replacement.

(b)

To determine

To find: whether of the following scenarios explain a geometric setting yes or not, If yes than define an appropriate geometric random variable.

Answer to Problem 110E

Yes, Geometric distribution

Explanation of Solution

There are four conditions for a geometric setting: independent trials, binary (success/ failure), probability of success is the same for every trial and the variable of interest is the number of trials required to get the first success.

Binary: it is satisfied, because of Success=get bag in the hole and Failure=do not get bag in the hole.

Independent trials: it is satisfied, because there are equally likely to obtain a bag into the hole on each toss (as the probability is 20%)

Probability of success: it is satisfied, because there is a 20% possibility of getting a bag into the hold and therefore the probability of success is 20%.

First success: it is satisfied, because of interested in the number of trials until he gets a bag in the hole, which is the first success.

Although all 4 conditions are satisfied, the given scenario explains a geometric setting.