What does the random variable for a binomial experiment of n trials measure? The random variable measures the mean of n trials. The random variable measures the number of successes out of n trials. The random variable measures the number of failures out of n trials. The random variable measures the standard deviation of n trials.

The random variable for a binomial experiment measures the number of successes out of n trials.

Explanation:

The random variable for a binomial experiment measures the number of successes out of n trials.

In a binomial experiment, each observation is independent and the probability of success doesn't change from trial to trial.  Also there is fixed number of observations or trials  and there exists only two outcomes, success or failure.

Example:

Toss a coin 10 times and measure the probability of getting 5 heads.

Since all the conditions are satisfied therefore, this experiment can be termed as binomial experiment.

The random variable measures the number of successes out of n trials.

Explanation:

A binomial random variable refers to the number of successes observed in repeated attempts at a binomial experiment. A binomial experiment, in turn, refers to the probability of repetition that can occur in independent tests.

An example of this can be seen in a situation where a coin is launched into the air twice. When the coin returns to the ground, there are only two possible outcomes: either the coin lands with the "face" side facing up, or with the "crown" side. Each of these launches is an experiment that has no relation to the result of the other, that is, they are independent and each one only presents two possible results that represent success or failure, depending on which side the person throwing the coin wants let it stay up. This experiment is the binomial experiment and the number of successes is the binomial random variable.

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