If X∼Normal(μ,σ2)X \sim \text{Normal}(\mu, \sigma^2)X∼Normal(μ,σ2), what is the distribution of the squared Mahalanobis distance 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)
Gamma(1,0.5)\text{Gamma}(1, 0.5)Gamma(1,0.5)
χ2(1)\chi^2(1)χ2(1)
Exponential(0.5)\text{Exponential}(0.5)Exponential(0.5)