Let S 1 2 and S 2 2 be the variances of independent random samples of sizes n 1 and n 2 selected from normally distributed populations with parameters ( 1 , 2 ) and ( 2 , 2 ), respectively Thus, the populations have different means, but a common variance 2 To estimate the common variance, we can co...

To show that the random variable n1 n2 2Sp22 follows a chisquare distribution with v n1 n2 2 degrees ...

Let S 1 2 and S 2 2 be the variances of independent random samples of sizes

Question:

Let S₁² and S₂² be the variances of independent random samples of sizes n₁ and n₂ selected from normally distributed populations with parameters (μ₁, σ²) and (μ₂, σ²), respectively. Thus, the populations have different means, but a common variance σ². To estimate the common variance, we can combine information from both samples and use the pooled estimator