Sonia Rowland

2022-10-01

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:

$Pr(Y=k)=p\cdot (1-p{)}^{k}\text{}\text{where}\text{}k=1,2,3\text{}\text{and}\text{}p=$ 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:

$Pr(Y=k)=p\cdot (1-p{)}^{k}\text{}\text{where}\text{}k=1,2,3\text{}\text{and}\text{}p=$ probability of success

Jasmin Hoffman

Beginner2022-10-02Added 6 answers

Step 1

If you use the geometric distribution as the number of failures until the first success then it is defined for $k\ge 0$. 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 $EX=1/p-1$. 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.

If you use the geometric distribution as the number of failures until the first success then it is defined for $k\ge 0$. 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 $EX=1/p-1$. 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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