Consider X∼N(μ,σ2)X \sim N(\mu, \sigma^2)X∼N(μ,σ2). What is the distribution of the normalized variable Z=X−μσZ = \frac{X-\mu}{\sigma}Z=σX−μ?
N(μ,1)N(\mu, 1)N(μ,1)
N(0,1)N(0, 1)N(0,1)
N(0,σ2)N(0, \sigma^2)N(0,σ2)
Standard Cauchy