{X1, X2, ..., Xn} which is independent and identical dis- Consider a random sample X =...

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{X1, X2, ..., Xn} which is independent and identical dis- Consider a random sample X = tributed (i.i.d.) from N(u1, o2) and another random sample Y = {Y1,Y2,..., Yn} which is independent and identical distributed (i.i.d.) from N(u2, 02). We know that the two random samples X and Y are independent. We also know that the sample size n = individual difference between two samples be D; = X; - Y;, i = 1, 2, ..., n. 16. Let the (a) Calculate the population mean and variance of D, where D = E D;. We denote the population mean and variance as 5 and o correspondingly. i3D1 (b) We observe that the sample mean and sample variance for X are T = 2.03 and s = 1.34. The sample mean and sample variance for Y are = 1.55 and s, that the sample covariance of X and Y is Say = three of s, s, and sæy to calculate the estimate of o?. = 1.71. We also observe n1 E (T1 – T)(yi – 7) = 0.5. Use all (c) We know that D N(Up, o). Obtain a 95% confidence interval for the variance of D, {X1, X2, ..., Xn} which is independent and identical dis- Consider a random sample X = tributed (i.i.d.) from N(u1, o2) and another random sample Y = {Y1,Y2,..., Yn} which is independent and identical distributed (i.i.d.) from N(u2, 02). We know that the two random samples X and Y are independent. We also know that the sample size n = individual difference between two samples be D; = X; - Y;, i = 1, 2, ..., n. 16. Let the (a) Calculate the population mean and variance of D, where D = E D;. We denote the population mean and variance as 5 and o correspondingly. i3D1 (b) We observe that the sample mean and sample variance for X are T = 2.03 and s = 1.34. The sample mean and sample variance for Y are = 1.55 and s, that the sample covariance of X and Y is Say = three of s, s, and sæy to calculate the estimate of o?. = 1.71. We also observe n1 E (T1 – T)(yi – 7) = 0.5. Use all (c) We know that D N(Up, o). Obtain a 95% confidence interval for the variance of D,

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