Question

Is the following X a Binomial random variable or not. Explain.

A) Suppose we randomly select 100 people to take part in a survey; we ask a person how many pets they have and we let X be their response.

B) Suppose we have a collection of books, 3 are adventure and 7 are a mystery. Suppose you randomly choose 3 to read and let X be the number of adventure selected.

Answer 1

1)People can have 0, 1, 2, or more pets. So there are more than two possible outcomes, so this cannot be
reduced to a binomial experiment. But If the question
was changed to Do you own a pet? then we could
do a binomial experiment as the outcome will be 2 ie yes or no .

2)yes this is a binomial distribution as there are exactly 2 outcome that is books being adventure or mystery .

So if x be the no. Of adventure books selected from all books , it is considered to be Binomial random variable