Let X 1 , ,X n1 be a random sample from an N ( 1 , 2 ) distribution and let Y 1 , ,Y n2 be a random sample from a N ( 2 , 2 ) distribution Show that the pooled estimator Is unbiased for 2 , where S 12 and S 2 2 are the respective sample variances i 2 2

Question: Let X 1 , . . . ,X n1 be a random sample from an N ( 1 , 2 ) distribution and

Let X₁, . . . ,X_n1 be a random sample from an N (μ₁, σ²) distribution and let Y₁, . . . ,Y_n2 be a random sample from a N (μ₂, σ²) distribution. Show that the pooled estimator

i 2 2

Is unbiased for σ², where S₁₂ and S₂² are the respective sample variances.

i 2 2

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