1a.) Let X₁,...,X₄ N(, ²). Suppose x = 2. Calculate a 99% confidence interval for in the cases:

i. = 3, i.e. it is known

ii. unknown, and S² = 9 1b.) Let X_1,...X₄ N(, ₁²) and Y_1,...Y₉ N(₂, ₂²). Suppose x = 2 and = 1. Calculate a 99% confidence interval for 1 2 in the following cases: i. ₁= 2 and ₂ = 3 (both known)

ii. _{1, 2} unknown, S²_X = 2 and S²_Y = 3