Suppose that X1, X2, . . . , Xm and Y1, Y2, . . . , Yn are

QUESTION:

Suppose that \(\mathrm{X}_{1}, \mathrm{X}_{2}, \ldots, \mathrm{X}_{\mathrm{m}}\) and

\(Y_{1}, Y_{2}, \ldots, Y_{n}\) are independent random samples, with the variables \(\mathrm{X}_{\mathrm{i}}\) normally distributed with mean \(\mu_{1}\) and variance \(\sigma_{1}^{2}\) and the variables \(\mathrm{Y}_{\mathrm{i}}\) normally distributed with mean \(\mu_{2}\) and variance \(\sigma_{2}^{2}\) The difference between the sample means, \(\bar{X}-\bar{Y}\) is then a linear combination of m + n normally distributed random variables and, by Theorem 6.3, is itself normally distributed.

Equation Transcription:

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Text Transcription:

X1, X2,...,Xm    

Y1, Y2,...,Yn    

Xi

\mu_1  

\sigma1^2

Y_i

\mu_2  

\sigma2^2  

\bar X - \bar Y  

E(\bar X - \bar Y )

V(\bar X - \bar Y )

\sigma1^2 = 2, \sigma2^2 = 2.5

(\bar X - \bar Y )

(\mu_1 - \mu_2)