Bernoulli and Binomial Distribution When a random process or experiment, called

Question

Bernoulli and Binomial Distribution

When a random process or experiment, called a trial, can result in only one of two mutually exclusive outcomes, such as dead or alive, sick or well, full-term or premature, the trial is called a Bernoulli trial.

The Bernoulli Process A sequence of Bernoulli trials forms a Bernoulli process under the following conditions.

1. Each trial results in one of two possible mutually exclusive, outcomes. One of the possible outcomes is denoted (arbitrarily) as a success, and the other is denoted a failure.

2. The probability of a success, denoted by p, remains constant from trial to trial. The probability of a failure, 1 - p, is denoted by q.

3. The trials are independent; that is, the outcome of any particular trial is not affected by the outcome of any other trial.

Explain why each of the following measurements is or is not the result of a Bernoulli trial,

A the gender of a newborn child

B the classification of a hospital patient’s condition as stable, critical, fair, good, or poor

C the weight in grams of a newborn child

Explanation / Answer

A. Here the gender of a newborn child is a bernoulli trial as there is only two possible genders and the probability of getting any gender is fixed which is 0.5.

(B) Here this problem defies that there are two mutually exclusive events. Here, there are variaous results possible i.e. stable, critical, fair , good and poor. so not a bernoulli trial.

(C) Here weight in grams is a continous event and there is no success or failure involved here. It is a measurable quantity so this is also not a benoulli trial.

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