The Standard Normal Distribution has mean equal to

Concept

For a normal random variable X ~ N(μ, σ2), μ is the centre and expected value, while σ2 measures spread.

Standardising uses Z = (X − μ)/σ; the standard normal distribution is the special case Z ~ N(0, 1).

Application

1. Read the parameters in N(0, 1): μ = 0 and σ2 = 1.

2. The requested mean is the location parameter μ, so its value is 0.

Cross-check

The standard normal density is symmetric about z = 0, and symmetry gives E[Z] = 0.

Therefore, the mean of the standard normal distribution is 0.