For Bernoulli distribution with probability p of success and q of a failure, the relation between mean and variance is -

Concept:

• Mean = μ = np
• \({\rm{Standard\;deviation}} = {\rm{\sigma }} = \sqrt {{\rm{npq}}} {\rm{\;}}\)
• Variance = npq

Where n = number of trials; p = probability of success; q = (1-p) = probability of failure

probability of an event lies between 0 and 1.

Calculation:

As we know, Mean = μ = np

Variance = npq 

⇒ Variance = μ × q

Probability of an event lies between 0 and 1.

Therefore 0 ≤ {p, q} ≤ 1

μ × q < μ

∴ Mean > Variance