Question: Let x n and s 2 n be the sample mean and variance for the sample {x 1 , x 2 , x 3 ,

Let x_n and s²_n be the sample mean and variance for the sample {x₁, x₂, x₃, . . . , x_n}, and let x_n+1 and s²_n+1be the sample mean and variance when we add a new observation x_n+1 to the sample.

Show that s²_n+₁can be computed from x_n+₁, x_n , and s²_n

Hint:

Show that ns²_n+1satisfies ns²_n+1 = (n 1)s²_n + (n/(n + 1 ))(x_n+1 x_n)²

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