Let X1, ...,Xm be a random sample from the N(1,2 1) distribution and let Y1, ...,Yn be a random sample from the N(2,2 2) distribution,

Let X1, ...,Xm be a random sample from the N(μ1,σ2 1) distribution and let Y1, ...,Yn be a random sample from the N(μ2,σ2 2) distribution, with Xi’s being independent from Yj ’s. Find the MLE of: (i) μ1,μ2,σ2 if σ1 = σ2 = σ. (ii) μ,σ2 1,σ2 2

where μ1 = μ2 = μ.