If X∼Normal(μ,σ2)X \sim \text{Normal}(\mu, \sigma^2)X∼Normal(μ,σ2), what is the distribution of the Mahalanobis distance squared D2=(X−μ)2σ2D^2 = \frac{(X-\mu)^2}{\sigma^2}D2=σ2(X−μ)2?
Normal(0,1)\text{Normal}(0, 1)Normal(0,1)
Chi-Squared(1)\text{Chi-Squared}(1)Chi-Squared(1)
Exponential(1/2)\text{Exponential}(1/2)Exponential(1/2)
Gamma(1,2)\text{Gamma}(1, 2)Gamma(1,2)