Question: Let X1, . .., Xn, Wi,.... W. be i.i.d. random variables that are normally distributed. Let Y, = Xi + W., denote by Xn, Wn

Let X1, . .., Xn, Wi,.... W. be i.i.d. random variables that are normally distributed. Let Y, = Xi + W., denote by Xn, Wn the sample means of Xi, Wi, and let SX,n, Swn be the sample variances of Xi, Wi, respectively. Which of the following is a valid 95% confidence interval for the mean of Y,? where z is the 0.975-quantile of the standard normal distribution. Question 4 (a) In + Wn - 22 SXn town, Xn + Wn + z-xintown. Vn Vn ( b ) | Xn + Wn - z Vox n town, Xn + Witz V x ntown Vn Vn n n (d) Xn - Spi, In + 2 5Am

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