Results 1 to 4 of 4

Math Help - Creating cumulative distribution function of Random variable.

  1. #1
    Newbie
    Joined
    Oct 2010
    Posts
    2

    Thumbs down Creating cumulative distribution function of Random variable.

    Electrons hit a circular plate with unit radius. Let X be the random variable representing
    the distance of a particle strike from the centre of the plate. Assuming that a particle is
    equally likely to strike anywhere on the plate,
    (a) for 0 < r < 1 find P(X < r), and hence write down the full the cumulative distribution
    function of X, FX;
    (b) find P(r < X < s), where r < s;
    (c) find the probability density function for X, fX.
    (d) calculate the mean distance of a particle strike from the origin.

    I have problem in crating CDF and finding mean distance.
    please help me.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Grand Panjandrum
    Joined
    Nov 2005
    From
    someplace
    Posts
    14,972
    Thanks
    4
    Quote Originally Posted by hotdone View Post
    Electrons hit a circular plate with unit radius. Let X be the random variable representing
    the distance of a particle strike from the centre of the plate. Assuming that a particle is
    equally likely to strike anywhere on the plate,
    (a) for 0 < r < 1 find P(X < r), and hence write down the full the cumulative distribution
    function of X, FX;
    (b) find P(r < X < s), where r < s;
    (c) find the probability density function for X, fX.
    (d) calculate the mean distance of a particle strike from the origin.

    I have problem in crating CDF and finding mean distance.
    please help me.
    The probability that P(X<r), 0<=z<=1 is the ratio of the area of a circle of radius r to that of one of radius 1. This is close to just the definition of a uniform distribution on the unit circle

    CB
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Oct 2010
    Posts
    2
    1)F(X)=(pi*r^2)/(pi*1)=r^2
    ok so,
    2)p(s>X>r)=(s^2-r^2)/r^2
    3)p.d.f =d(F(X))/dx=2X
    4)????
    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 hotdone View Post
    1)F(X)=(pi*r^2)/(pi*1)=r^2
    ok so,
    2)p(s>X>r)=(s^2-r^2)/r^2
    3)p.d.f =d(F(X))/dx=2X
    4)????
    \displaystyle \bar{x}=\int_0^1 x p(x)\;dx

    CB
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Distribution function of a random variable X
    Posted in the Advanced Statistics Forum
    Replies: 5
    Last Post: March 15th 2011, 03:57 PM
  2. Replies: 2
    Last Post: October 14th 2010, 04:02 PM
  3. Random Variable Distribution Function
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: October 4th 2010, 09:17 PM
  4. Mean and variance of random variable distribution function F(z)
    Posted in the Advanced Statistics Forum
    Replies: 3
    Last Post: October 23rd 2009, 02:15 AM
  5. Replies: 3
    Last Post: October 15th 2008, 11:21 PM

Search Tags


/mathhelpforum @mathhelpforum