Consider a mixture distribution of two triangle distributions, where component density ω i is centered on µ i and has “halfwidth” w i , according to: (a) Assume P(ω 1 ) = P(ω 2 )=0.5 and derive the...

Consider a mixture distribution of two triangle distributions, where component density ω_i
is centered on µ_i
and has “halfwidth” w_i, according to:

(a) Assume P(ω₁) = P(ω₂)=0.5 and derive the equations for the maximum likelihood values ˆµi and ˆwi, i = 1, 2.

(b) Under the conditions in part (a), is the distribution identifiable?

(c) Assume that both widths w_i
are known, but the centers are not. Assume, too, that there exist values for the centers that give non-zero probability to each of the samples. Derive a formula for the maximum-likelihood value of the centers.

(d) Under the conditions in part (c), is the distribution identifiable?