Results 1 to 8 of 8

Math Help - a continuous random variable with probability density function

  1. #1
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35

    Question a continuous random variable with probability density function

    suppose that X is a continuous random variable with probability density function given by

    f(X) = x^2 + (2/3)x +(1/3) for <or = x <or = c

    (a) what must be the value of c
    assuming this value of c , do the following :-

    b) plot f(x)
    c) compute and plot F(x)
    d)compute p(1/3 <or = X < or = 2/3 ) , E(X) , var (X)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Is the interval (0,c)?
    Note that for continuous random variables
    you can use (0,c) as well as [0,c]

    Just integrate and set the probability equal to 1, to find c.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35

    Lightbulb

    intergration from 0 to c x^2 + (2/3)x + 1/3

    c
    x^3 / 3 + x^2 /3 + x/3 |
    0


    c^3/ 3 + c^2 / 3 + c /3 =1 multiple by 3


    c^3 + c^2 + c = 3

    c =1


    is that answer is right
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35

    Question

    and for part b) plot f(x)

    do i to choose random number an substitute at the integrated equation ?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    divide by c-1 into your cubic, to find the other two roots
    most likely c=1 is the only real root.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    Quote Originally Posted by compufatwa View Post
    and for part b) plot f(x)

    do i to choose random number an substitute at the integrated equation ?

    plot x vs f(x),

    and F(x)=\int_0^x f(t)dt for all x in (0,c)
    F=0 if x<c
    F=1 if x>c.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35
    integration from 0 to x x^2 + 2/3 x + 1/3
    x
    [x^3 / 3 + 1/3 x^2 + 1/3 x |
    0
    x^4 /3 + 1/3 x^3 + 1/3 x^2 - 0

    i do n't know if that what u mean u not
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Junior Member
    Joined
    Oct 2007
    From
    Egypt
    Posts
    35
    i think i have to take the equation that i have already integrated it and integrate iy a gain with interval 0 to x
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 2
    Last Post: November 11th 2011, 05:06 AM
  2. Replies: 1
    Last Post: September 3rd 2010, 10:51 PM
  3. Replies: 3
    Last Post: October 15th 2008, 11:21 PM
  4. Replies: 1
    Last Post: April 24th 2008, 11:41 AM
  5. Continuous Random Variable and Density Function
    Posted in the Advanced Statistics Forum
    Replies: 6
    Last Post: November 2nd 2007, 05:57 AM

Search Tags


/mathhelpforum @mathhelpforum