Suppose that we have a random sample We plan to use to

QUESTION:

Suppose that we have a random sample \(X_1,\ X_2,\ldots,\ X_n\)  from a population that is \(N\left(\mu, \sigma^{2}\right)\). We Plan to use \(\hat{\Theta}=\sum_{i=1}^{n}\left(X_{1}-\bar{X}\right)^{2} / c\) to estimate \(\sigma^{2}\). Compute the bias in \(\hat{\Theta}\) as an estimator of \(\sigma^{2}\) as a function of the constant c.

Equation Transcription:

Text Transcription:

X_1, X_2,..., X_n

N(mu,sigma^2)

Theta hat=sum i-1 n (X_1-X bar)^2 /c

sigma^2

Theta hat

sigma^2