Results 1 to 5 of 5

Math Help - The mean and Variance!

  1. #1
    Newbie
    Joined
    Feb 2009
    Posts
    3

    The mean and Variance!

    Hello,

    I need some help with this maths problem and I would appreciate if I can have a solution a.s.a.p cause I have to hand in my paper today before midnight.

    The problem is about the mean and variance. Here it is:"a continuous random variable X is defined for 0< = X < = 2 and has a probability density function given by f(x)=|1-x|. Calculate the mean and variance of this continous random variable"

    '<=' - means greater equal than...

    THANK YOU VERY MUCH...

    Tom
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Moo
    Moo is offline
    A Cute Angle Moo's Avatar
    Joined
    Mar 2008
    From
    P(I'm here)=1/3, P(I'm there)=t+1/3
    Posts
    5,618
    Thanks
    6
    Hello,
    Quote Originally Posted by adelante View Post
    Hello,

    I need some help with this maths problem and I would appreciate if I can have a solution a.s.a.p cause I have to hand in my paper today before midnight.

    The problem is about the mean and variance. Here it is:"a continuous random variable X is defined for 0< = X < = 2 and has a probability density function given by f(x)=|1-x|. Calculate the mean and variance of this continous random variable"

    '<=' - means greater equal than...

    THANK YOU VERY MUCH...

    Tom
    So the pdf is |1-x| if x is between 0 & 2.

    \mathbb{E}(X^k)=\int_0^2 x^k f(x) ~dx
    that's a formula you should know...


    So \mathbb{E}(X)=\int_0^2 x |1-x| ~dx
    in order to compute this integral, split it into two integrals : one with the domain where 1-x is positive (and hence |1-x|=1-x), one with the domain where 1-x is negative (and hence |1-x|=-(1-x)=x-1)

    Same thing : \mathbb{V}ar(X)=\mathbb{E}[(X-\mathbb{E}(X))^2]=\int_0^2  (x-\mathbb{E}(X))^2 |1-x| ~dx
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Feb 2009
    Posts
    3
    Hey dude,

    Thank you very much again...


    Tom
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    You should use the short cut formula for the variance
    \sigma^2=E(X^2)-(EX)^2
    and you need to break this integral into two pieces,
    from (0,1) and (1,2).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Feb 2009
    Posts
    3
    Actually I tried both of them, but thank you for your hint.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Help with variance
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: September 3rd 2011, 01:53 AM
  2. variance of the sample variance
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: February 8th 2011, 08:35 PM
  3. How to get new variance given old variance and average
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: November 23rd 2010, 05:39 AM
  4. Variance Help
    Posted in the Statistics Forum
    Replies: 2
    Last Post: August 23rd 2009, 01:22 PM
  5. Variance of the population variance.
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: November 10th 2008, 09:07 AM

Search Tags


/mathhelpforum @mathhelpforum