What does N(0,1) denote in the context of standard normal distribution?

What does N(0,1) denote in the context of standard normal distribution?

• A. Normal distribution with mean 0 and standard deviation 1
• B. Normal distribution with mean 1 and standard deviation 0
• C. Uniform distribution on [0,1]
• D. Exponential distribution with rate 1

Answer: (A)

This denotes the standard normal distribution: a normal distribution centered at zero with unit spread. In the notation N(μ, σ^2), μ is the mean and σ^2 is the variance; here the variance is 1, so the standard deviation is also 1. This is the canonical normal used to standardize any normal variable by transforming Z = (X − μ)/σ, which then follows N(0,1). The probability density function is f(z) = (1/√(2π)) exp(-z^2/2), and probabilities are read from the standard normal CDF Φ(z).

This denotes the standard normal distribution: a normal distribution centered at zero with unit spread. In the notation N(μ, σ^2), μ is the mean and σ^2 is the variance; here the variance is 1, so the standard deviation is also 1. This is the canonical normal used to standardize any normal variable by transforming Z = (X − μ)/σ, which then follows N(0,1). The probability density function is f(z) = (1/√(2π)) exp(-z^2/2), and probabilities are read from the standard normal CDF Φ(z).