The first moment about origin of binomial distribution is

Binomial distribution:

Let p is the probability that an event will happen in a single trail (called the probability of success) and

q = 1 – p is the probability that an event will fail to happen (probability of failure)

The probability that the event will happen exactly r times in n trails (i.e. x successes and n – r failures will occur) is given by the probability function

where the random variable X denotes the number of successes in n trials and r = 0, 1, 2, … n

For Binomial distribution,

Mean = μ = np

Variance = σ² = npq

Standard deviation = σ = √(npq)

The expected value is sometimes known as the first moment of a probability distribution. The expected value is comparable to the mean of a population or sample.

Therefore, the first moment about the origin of the binomial distribution is,

Mean = μ = np