Results 1 to 5 of 5

Math Help - [SOLVED] Mathematical Expectation (Continuous Prob Dist.)

  1. #1
    Junior Member
    Joined
    Nov 2009
    Posts
    60

    Question [SOLVED] Mathematical Expectation (Continuous Prob Dist.)

    4.56 walpole

    The total time, measure in units of 100 hours, that a teenager runs her stero set over a period of one year is a continuous random variable X that has the density function:

    f(x) = x, 0<x<1
    2-x, 1<=x<2
    0, elsewhere

    Evalue the mean of the random variable Y=60X^2 + 39X , where Y is equal to the number of kilowatt hours expended annually.

    what i did was :
    E(X) = int 0-1 x dx + int 1-2 (2-x) dx
    E(X^2) = int 0-1 X^2 dx + int 1-2 x(2-x) dx

    and then E(Y) = 60((EX^2)) + 39 (E(X))

    but it doesn't add up to 109 (answer)

    what did i do wrongly ?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by hazel View Post
    4.56 walpole

    The total time, measure in units of 100 hours, that a teenager runs her stero set over a period of one year is a continuous random variable X that has the density function:

    f(x) = x, 0<x<1
    2-x, 1<=x<2
    0, elsewhere

    Evalue the mean of the random variable Y=60X^2 + 39X , where Y is equal to the number of kilowatt hours expended annually.

    what i did was :
    E(X) = int 0-1 x dx + int 1-2 (2-x) dx Mr F says: You got 1, right?

    E(X^2) = int 0-1 X^3 dx + int 1-2 x^2(2-x) dx Mr F says: Note the corrections in red. So E(X^2) = 7/6.

    and then E(Y) = 60((EX^2)) + 39 (E(X))

    but it doesn't add up to 109 (answer)

    what did i do wrongly ?
    Fix the mistake and you will get 109.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2009
    Posts
    60

    Question

    but why is there an additional x ?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Flow Master
    mr fantastic's Avatar
    Joined
    Dec 2007
    From
    Zeitgeist
    Posts
    16,948
    Thanks
    5
    Quote Originally Posted by hazel View Post
    but why is there an additional x ?
    Surely you know that E(X^n) = \int x^n f(x) \, dx.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Junior Member
    Joined
    Nov 2009
    Posts
    60
    urgh. oh yes. now i got it.
    thanks.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Continuous uniform dist. question
    Posted in the Statistics Forum
    Replies: 2
    Last Post: November 19th 2011, 06:45 AM
  2. Replies: 6
    Last Post: November 14th 2009, 11:23 PM
  3. HEP ME>>>> Prob Dist
    Posted in the Statistics Forum
    Replies: 1
    Last Post: March 4th 2008, 08:23 PM
  4. Normal Dist Prob
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 4th 2007, 05:25 AM
  5. Prob Dist.. just some clarity please.
    Posted in the Statistics Forum
    Replies: 7
    Last Post: April 27th 2006, 01:46 AM

Search Tags


/mathhelpforum @mathhelpforum