1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: Normal random variables (3rd)

  1. Mar 29, 2009 #1
    1. The problem statement, all variables and given/known data
    Let Z be a standard normal random variable and [tex]\alpha[/tex] be a given constant. Find the real number x that maximizes P(x < Z < x + [tex]\alpha[/tex])/

    2. Relevant equations

    3. The attempt at a solution
    Looking at the standard normal tables, it seems obvious to me that x=0 gives the largest spread regardless of the value of the constant, but I am not sure how to find this computationally. Can anyone give me a hint on what direction to take? Thanks for any help.

    I got most of the rest of the homework done, but the three I just posted really have me stumped.
  2. jcsd
  3. Mar 30, 2009 #2


    User Avatar
    Homework Helper

    Looking at the level of your other posts, I'm assuming you have a calculus background? If not - sorry.
    Note that

    P(x \le X \le x + \alpha) = \Phi(x+\alpha) - \Phi(x)

    If this is maximized then its derivative (with respect to [tex] x [/tex]) is zero. Find the derivative, and work with that.
  4. Mar 30, 2009 #3
    I took the calculus series as a freshman in college 19 years ago. I am struggling through a few higher level courses in my pursuit of a 7-12 integrated mathematics teaching degree. This homework is for an advanced statistics and probability class through independent study at LSU. I have abstract/modern algebra after this and I will have my math prereqs completed. I bought a calculus book to refresh my memory on some things while working through these classes. Number Theory is what brought me to these boards in the first place!

    I am going to go see if I can figure it out from what you gave me. Thanks for the hint, I hope!
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook