Thread: Stats review

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)

Originally Posted by plm2e

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.

[snip]

(since the X's are i.i.d) where G(x) is the cdf of X.

And you should know that for .

thanks for the help on prob 1.

Originally Posted by plm2e

[snip]

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

[snip]

From the definition: .

From the definition: .

From the definition: .