Central Limit Theorem: Sample Question

Please see the attached file.

Please see the attached file.

Problem:
Suppose that X1, X2, … Xn and Y1, Y2, … Yn are independent random samples from populations with means 1 and 2 and variances 12 and 22 respectively. Show that the random variable satisfies the conditions of Thm. 7.4 and thus that the distribution function of Un …

The expert examines central limit theorem for sample questions.