Results 1 to 4 of 4

Math Help - Standard Normal Distrbution question

  1. #1
    Newbie
    Joined
    Dec 2010
    Posts
    6

    Standard Normal Distrbution question

    Hello All,

    I've found this forum to be a lot of help. The answers provided to my last question were helpful and I'm hoping I can get similar help for this question.

    Y has the standard normal distribution.

    1. Determine the distribution function of |Y|, the absolute value of Y.

    2. Determine the probability density function of
    |Y|

    3. Find P(
    |Y|>1.70).

    For part 1, I did this:

    P(|Y|) ≤ x)= P(−x ≤ Y≤ x) = ϕ(x) ϕ(-x)
    = ϕ(x) -(1 − ϕ(x) ) = 2ϕ(x) − 1 .

    Does that look correct?

    For 2, this is my work,

    f(x)= d
    P(|Y|) ≤ x)= 2ϕ'(x)
    dx

    Which is equal to 2*(1/
    √2π)*e^(-x^2/2)

    Is my work right for this?

    I'm not sure about how I would go about doing 3, so all tips are appreciated. Thanks.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    This is tough to type with an I(dot) pad, but the prob of abs y greater than 1.7 is twice that y is greater than 1.7
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by hwill205 View Post
    Hello All,

    I've found this forum to be a lot of help. The answers provided to my last question were helpful and I'm hoping I can get similar help for this question.

    Y has the standard normal distribution.

    1. Determine the distribution function of [FONT=verdana, geneva, helvetica][SIZE=2][COLOR=#000000]|Y|, the absolute value of Y.
    F_{|Y|}(u)=Pr(|Y|<u)=Pr(-u<Y<u),\ \mbox{ when } u>0 \mbox{ and } 0 \mbox{ otherwise }

    Now write the right most probability in terms of the cumulative standard normal. Which is what you did, so yes.

    CB
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by hwill205 View Post
    2. Determine the probability density function of [/COLOR][/SIZE][/FONT][FONT=verdana, geneva, helvetica][SIZE=2][COLOR=#000000]|Y|
    Differentiate the cumulative distribution you get in part (1). Again this is what you did so yes.

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Normal Distrbution , how to find sign of z
    Posted in the Statistics Forum
    Replies: 1
    Last Post: December 1st 2011, 05:04 AM
  2. standard normal random variable question
    Posted in the Advanced Statistics Forum
    Replies: 4
    Last Post: April 2nd 2011, 03:20 AM
  3. Standard normal R.V. question
    Posted in the Statistics Forum
    Replies: 1
    Last Post: October 26th 2009, 07:29 PM
  4. standard normal
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: November 4th 2007, 04:27 AM
  5. standard normal question
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 4th 2006, 01:19 AM

Search Tags


/mathhelpforum @mathhelpforum