An experiment is conducted with 5 people and the number of calls made to reach the banking officer is recorded.(they are asked to retry if the call-back service is reached).The number of calls made to reach the banking officer is recorded for each participant and are as follows: 5, 0, 1, 0, 0

Sonia Rowland 2022-10-01 Answered
Geometric distribution-Calculation of probability of success
I saw a question on geometric distribution.
A bank is reviewing its telephone banking division and tries to find how soon/easily a customer can talk to a phone-banking officer. When a customer calls, the phone rings for 12 times before getting to the call-back services.
An experiment is conducted with 5 people and the number of calls made to reach the banking officer is recorded.(they are asked to retry if the call-back service is reached).The number of calls made to reach the banking officer is recorded for each participant and are as follows:
- 5
- 0
- 1
- 0
- 0
In this experiment, what is the probability of success(p of a geometric distribution)? Is it 1/2 (because it is equally likely to reach the officer as reaching the call back service) or is it 3/5( 3 participants out of 5 have reached the bank officer in the first attempt without any failure) ?
Geometric distribution used for modeling the number of failures until the first success:
P r ( Y = k ) = p ( 1 p ) k   where   k = 1 , 2 , 3   and   p = probability of success
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Answers (1)

Jasmin Hoffman
Answered 2022-10-02 Author has 6 answers
Step 1
If you use the geometric distribution as the number of failures until the first success then it is defined for k 0. A possible way of estimating the p is by the method of moments.
Step 2
You know that your distribution is a X Geo(p) wso its mean is E X = 1 / p 1. You can find the mean for your sample and by equating to that of X get an estimating for p.
Be aware that you can only estimate p, not find it.
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