Consider a random sample Y1, Y2, …, Yn from a continuous population with mean E(Yi) = μ and fini

Name: Consider a random sample Y1, Y2, …, Yn from a continuous population with mean E(Yi) = μ and finite variance V(Yi) = σ^2. Show that the estimator (1)/(n)∑i=1^n (Yi - Y)^2 is a biased estimator for σ^2.
Uploaded: 2023-06-21T07:41:57-08:00
Duration: 4 min 12 s
Channel: Sri K
Description: Consider a random sample Y1, Y2, …, Yn from a continuous population with mean E(Yi) = μ and finite variance V(Yi) = σ^2. Show that the estimator (1)/(n)∑i=1^n (Yi - Y)^2 is a biased estimator for σ^2.

Here in the first part, if i is not equal to j, then expectation of xi and xj is equal to expect

Question

Consider a random sample $Y_1, Y_2, \dots, Y_n$ from a continuous population with mean $E(Y_i) = \mu$ and finite variance $V(Y_i) = \sigma^2$. Show that the estimator $\frac{1}{n}\sum_{i=1}^n (Y_i - \overline{Y})^2$ is a biased estimator for $\sigma^2$.

          Consider a random sample $Y_1, Y_2, \dots, Y_n$ from a continuous population with mean $E(Y_i) = \mu$ and finite variance $V(Y_i) = \sigma^2$. Show that the estimator $\frac{1}{n}\sum_{i=1}^n (Y_i - \overline{Y})^2$ is a biased estimator for $\sigma^2$.

Consider a random sample Y1, Y2, …, Yn from a continuous population with mean E(Yi) = μ and finite variance V(Yi) = σ^2. Show that the estimator (1)/(n)∑i=1^n (Yi - Y)^2 is a biased estimator for σ^2.

Added by Paula G.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

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Consider a random sample Yâ‚, Yâ‚‚, ..., Yâ‚™ from a continuous population with mean E(Y) = Î¼ and finite variance V(Y) = ÏƒÂ². Show that the estimator SÂ² = 1/(n-1) Î£(Yáµ¢ - È²)Â² is a biased estimator for ÏƒÂ².