Question

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

Answer 1

The probability of getting exactly X successes in n trials is given by the Probability Mass Function.

$p(X) = \binom{n}{X}p^{X}.(1-p)^{n-X}$

Where binomial coefficient is

$\binom{n}{X} = \frac{n!}{X!(n-X)!}$

With the help of this binomial probability distribution we find probability of X number of success in n number of trials of a random variable.

So the random variable for a binomial experiment of n trials measures the number of successes out of n trials. 1st option is correct.