Which of the following is not an example of a Bernoulli random variable? X = whe

Question

Which of the following is not an example of a Bernoulli random variable?

X = whether or not the next person in the checkout at a grocer spends more than $50

C = the gender of a person having surgery for coronary artery disease

W = whether or not a light bulb works

U = the number of people who pre-register for an engineering class

X = whether or not the next person in the checkout at a grocer spends more than $50

C = the gender of a person having surgery for coronary artery disease

W = whether or not a light bulb works

U = the number of people who pre-register for an engineering class

Explanation / Answer

Bernoulli distribution are special type of binomial distribution where there are only two outcomes i.e p and q(1-p). Bernoulli distribution is restricted to only one trial (n=1), that is why it is a special case of binomial distribution.

From the given variables, only those will be bernoulli random variable where outcomes will be binomial and trial will be 1. Hence using this theoram following is the result of question-

X : This is a bernoulli random variable because here n=1(only restricted to next person) and outcome is binomial(whether he will spend more than $50 or not)

C : This is a bernoulli random variable because here n=1(only restricted to the one person who is having surgery) and outcome is binomial i.e wheter the person is male or female

W: This is also a bernoulli random variable since n=1 i.e. it is about a single light bulb and outcome is binomial i.e. whether it works or not

U : This is not a bernoulli random variable since here n is not restricted to 1

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