Ch 9 - 17E

QUESTION:

Suppose that \(X_{1}, X_{2}, \ldots, X_{n}\) and \(Y_{1}, Y_{2}, \ldots, Y_{n}\) are independent random samples from populations with means \(\mu_{1}\) and \(\mu_{2}\) and variances \(\sigma_{2}^{1}\) and \(\sigma_{2}^{2}\), respectively. Show that \(\bar{X}-\bar{Y}\) is a consistent estimator of \(\mu_{1}-\mu_{2}\).

Equation Transcription:

 -

Text Transcription:  

X_1, X_2, …., X_n

Y_1, Y_2, …., Y_n

mu_1

mu_{1}

sigma_{2}^{1}

sigma_{2}^{1}

bar{X} - bar{Y}

mu_{1} - mu_{2}