examples of if a solution is binomial or not binomial exampl

Solution

Definition. A discrete random variable X is a binomial random variable if:

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Example of a binomial solution -

A coin is weighted in such a way so that there is a 70% chance of getting a head on any particular toss. Toss the coin, in exactly the same way, 100 times. Let X equal the number of heads tossed.

So, the distribution of \'X\' will be binomial.

X is a binomial random variable, because:

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Example of a non-binomial solution -

A college administrator randomly samples students until he finds four that have volunteered to work for a local organization. Let X equal the number of students sampled.

So, X is not a binomial distribution because -

The number of trials n was not fixed in advance, and X does not equal the number of volunteers in the sample.