Geometric distribution-Calculation of probability of successI 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- 0In 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

Question

Geometric distribution-Calculation of probability of successI 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- 0In 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

Jasmin Hoffman · Accepted Answer

Step 1If 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 2You 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.

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

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