Assume we have two independent population random variables, X and Y. Let X N(ux, 60) and Y nx = 15 and m = ny = 8 having a = 70.1, j = 75.3. Then construct one-sided 95% N(uy, 40). We have samples from each population with n =

If X and Y are random variables with variances o = 3 and σ = 9, X and Y are not independent, and oxy = 1, then find the variance of the random variable Z = -9X+8Y - 7.

Suppose that X₁, X₂, Xn and Y₁, Y2, . Yn are independent random samples from populations with means ₁ and ₂ and variances of and o2, respectively. Show that X - Y is a consistent estimator of μ₁ - 2.

Question 8. This question is similar to Exercise 11 on page 363 of your textbook. Let t be a t-random variable. P(ta) = 0.05 and 65 degrees of freedom. Use Excel function =t.inv to find a. ii. Use Excel function =t.dist to find P(t 2.16) with df =23 This is a fill-in-blank question. Do not show your work. Write your answer with the format of #.###, #.####, #.####. The first number is for (i), the second number is for (ii), and so on.