hello, I am working on a review sheet to get ready for a stats test. I am not finding any examples in my text book to help me. I have a few questions and I am looking for an explanation, not just the answer. Please help me out if you can.
1. Let X1, X2, ... ,Xn be independent random variables, each having a uniform distribution over (0,1). Let M = maximum (X1, X2, ... ,Xn). Show that the distribution function of M, FM(.) is given by: FM(x) = x^n , 0< x < 1.
2. The joint density of X and Y is given by:
f(x,y) = [e^(-x/y)e^(-y)]/y , 0 < x < ¥, 0 < y < ¥
Show that E[XlY=y] = y
3. If X and Y are both discrete, show that ∑x Pxly (xly)= 1 for all such that PY(y) > 0.
4. Show that
a. Cov (X,Y) = Cov (X,E[YlX])
b. suppose, that, for constants a and b, E[YlX] = a + bX
show that b= Cov(X,Y)/Var(X)