Suppose X 1 ,X 2 , , X n1 is a random sample from a N(, 1) distribution Besides these n 1 observable items, suppose there are n 2 missing items, which we denote by Z 1 , Z 2 , , Z n 2 Show that the first step EM estimate is where (0) is an initial estimate of and n n 1 n 2 (1) nT n() n

Question: Suppose X 1 ,X 2 , . . . , X n1 is a random sample from a N(, 1) distribution. Besides these n 1

Suppose X₁,X₂, . . . , X_n1 is a random sample from a N(θ, 1) distribution. Besides these n₁ observable items, suppose there are n₂ missing items, which we denote by Z₁, Z₂, . . ., Z_n₂ . Show that the first-step EM estimate is

(1) nT + n() n

where ^{^}θ⁽⁰⁾ is an initial estimate of θ and n = n₁ + n₂.

(1) nT + n() n

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