I am familar with the high level concepts of expectation, correlation, and variance but forgot how to do the derivations. Would you give me a few pointers on how to approach this problem?

1.4 Question 2: Correlation Recall that the correlation between random variables X and Y is dened as T(Xa Y) = E(Xsu}fsu) where X3\" is X in standard units and mm is Y in standard units. In this exercise you will show that 1 S r(X , Y) s 1. It will help to recall properties of random variables in standard units, so please do that before getting started. Correlation is an expected product. We are much better at working with sums and squares than with products. So recall an elementary fact that connects sums, squares, and products: (a + b)2 = a2 + 2a?) + b2. Hint: Refer to Slide 33 of Lee 20 to recall that ]E(Xu) = E022\") = 1. 1.4.1 Question 2a Consider the nonnegative random variable V = (X 3\" + Y\")? Find ]E(V) and hence show that r(X , Y) 2 1. Write your answer here, replacing this teat. 1.4.2 Question 2b Use W = (Xw Km)? to show that r(X, Y) s 1. Write your answer here, replacing this teat