Statistics: Using a PDF function

[Xyius]

Homework Statement

I am doing a practice final exam in preparation of my actual final exam next week. Here is the link. I am doing problem number 2.

http://www.math.stevens.edu/~ifloresc/Teaching/2011-2012/MA222S12/Final_Exam_Summer2011.pdf

The Attempt at a Solution

So this seems pretty straight forward starting out, but I noticed that the PDF does not integrate to 1 as it should. So I redefined the function so that it does. Was this the correct thing to do? Because later in the problem I have more issues with finding the standard deviation. It appears as though I get a negative variance! Here is my work..

http://img43.imageshack.us/img43/9818/work1hm.jpg

If anyone could help me I would be so thankful!

 

[Ray Vickson]

Homework Statement

I am doing a practice final exam in preparation of my actual final exam next week. Here is the link. I am doing problem number 2.

http://www.math.stevens.edu/~ifloresc/Teaching/2011-2012/MA222S12/Final_Exam_Summer2011.pdf

The Attempt at a Solution

So this seems pretty straight forward starting out, but I noticed that the PDF does not integrate to 1 as it should. So I redefined the function so that it does. Was this the correct thing to do? Because later in the problem I have more issues with finding the standard deviation. It appears as though I get a negative variance! Here is my work..

http://img43.imageshack.us/img43/9818/work1hm.jpg

If anyone could help me I would be so thankful!

Question 2 has a serious typo. The function f(x) as described goes negative for x > 1/2, so cannot possibly be a legitimate pdf.

RGV

 

[Xyius]

Thats what I thought! But I wasn't sure! I hope to god he didn't ACTUALLY give this PDF in a final.

 

[Xyius]

Since I already posted the questions, I REALLY do not understand number 6. They didn't give the number of n, so how can I find the expected value when n is large??