Question

If X is a Binomial then give the Shortcut Equations:

a) MEAN
b) Variance
c) Standard Devation

Answer 1

The mean of a Binomial distribution is given by μ = np, variance by σ² = npq, and standard deviation by σ = √npq, where 'n' is the number of trials, 'p' is the probability of success, and 'q' is the probability of failure.

Step-by-step explanation:

If X is a Binomial distributed random variable, then the shortcut equations to calculate the mean (μ), variance (σ²), and standard deviation (σ) of X are as follows:

• The mean (μ) is given by the equation μ = np.
• The variance (σ²) is given by the equation σ² = npq.
• The standard deviation (σ) is the square root of the variance, which can be written as σ = √npq.

Here, 'n' represents the number of trials, 'p' is the probability of success on a single trial, and 'q' is the probability of failure (which is 1 - p).