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...

Let X 1 , . . . ,X n1 be a random sample from an N (

Question:

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

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

Distribution
The word "distribution" has several meanings in the financial world, most of them pertaining to the payment of assets from a fund, account, or individual security to an investor or beneficiary. Retirement account distributions are among the most...