# Is it binomial or normal?

Binomial Distribution:

A binomial distribution is a common probability distribution that occurs in practice. It arises in the following situation:

There are n independent trials.

Each trial results in a "success" or "failure"

The probability of success in each and every trial is equal to 'p'.

If the random variable X counts the number of successes in the n trials, then X has a binomial distribution with parameters n and p.

X ~ Bin (n, p).

Properties of Binomial distribution:

If X ~ Bin (n, p), then the probability mass function of the binomial distribution is

f (x) = P (X =x) =

^{n}C_{r}p^{x}(1 - p)^{n-x}for x = 0, 1, 2, 3,...,n

Mean E (X) = μ = np.

Variance (σ

^{2}) = np(1 - p).Hence, option (D) is correct.

Regards

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