Answer all.

Part One: Prominent Student Right case. Review the following case short IRAC summary for two of them.

1 Sweatt v Painter (1954) (Separate but equal)

2 Southeastern Community College V Davis (1979) Section 504 0f the Rehabilitation Act of 1973

3 Regents of the University of Michigan V. Ewing ( Due process)

4 Papish V Board of curators of the University of Missouri (1973) (Free Speech).

5 Healy V James (1972) (Free Speech)

Part Two: Current Status of Prominent cases for each of the cases you chose answer the following questions.

1 What are your thought on the outcome of the case?

A Do you think the judges made the right decision? Why or Why not?

2 How have the issues in this case raised been addressed more recently? either in legislation or current events give detailed examples.

3 Do you think the issues of this case are still relevant today? How?

List references and sources to compare to.

244 SOME SPECIAL DISTRIBUTIONS It is easy to show (Problem 2) that cov(X. Y) = a/x, so that var(2) = 2[1 + (a/x)] If Z is normal, its MGF must be (12) Next we compute the MGF of Z directly from the joint PDF (10). We have - + +12F() - 112F()- 1If()f()dxdy = +a "[2F() - 11/()dx Now "(2F() - 1/()dx = -2 "[1 - F(x)/(x)dx + 'n exp -s(x2 + (u + x)? - zx] expl-87 /2 + (v - 1)2/4] expl-[x + (# - 0)/217) -dx du du (13) where Z, is an A(0. 1) RV. It follows that (14) 1+a(1-28/21- #21)"I| Exercise 2.15 Bivariate normal a) In the bivariate normal distribution (see Example 2.73), show that if E is a diagonal matrix then (X1, X2) are also independent and follow univariate normal distributions. b) Assume that Z, and Z2 are independent standard normal random vari- ables. Now let X and Y be defined by X = an121+ CI. Y = 012Z1 + 022Z2 + C2. Show that an appropriate choice of a11, 412, 422, C1, C2 can give any bivariate normal distribution for the random vector (X, Y), i.e. find a11, #12, 022, C1, 62 as a function of #x, My and the elements of E. Note that Eij = Cov(X, X;) (i.e. here 212 = E21 = Cov(X, Y)), and that any linear combination of random normal variables will result in a random normal variable.1 5 points X and Y are independent bivariate Gaussian random variables with ux = My = 0 andox = oy = 1. Let W = [X + Y|. What is the CDF FW (w)? O FW(w) = 20(w) -1 O Fw (w) = 20(w/V2) - 1 O FW ( w ) = 20 ( w / 2 ) - 1 Jo w