Results 1 to 5 of 5

Math Help - Mean of random variable

  1. #1
    Newbie
    Joined
    Mar 2008
    Posts
    18

    Mean of random variable

    Hello guys, we are starting random variables and I know that the mean of a random variable is the function times the probability for all x's (right?), but I am lost with the next two problems. Any help on number 1 would be greatly appreciated, full answer or not. For number 2 I am totally lost.

    1. What is the mean of X which has the following density function?
    f X (x) = 1/C; for: 0 <= x <= 7
    Hint: Find the numerical value of C


    2. Consider the probability density function given by:
    P X (x) = lambda/2; for: 0<= x <=2
    P X (x) = (1 - lambda)/4; for: 2<= x <=6

    This is a mixture of two uniform distributions. a)Sketch P X (x) for lambda=0.5. b) Sketch P X (x) for lambda=0.333. c) In a random sample from P X (x), 60% of the values were between 0 and 2. What would be an estimate for the value of lambda?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,966
    Thanks
    1785
    Awards
    1
    The total probability mass must be one.
    So find C such that \int\limits_0^7 {\frac{1}{C}dx}  = 1.

    For #2 do similarly.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Mar 2008
    Posts
    18
    thanks a lot
    could you elaborate a bit on problem #2 please?
    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 enmascarado View Post
    Hello guys, we are starting random variables and I know that the mean of a random variable is the function times the probability for all x's (right?), but I am lost with the next two problems. Any help on number 1 would be greatly appreciated, full answer or not. For number 2 I am totally lost.

    1. What is the mean of X which has the following density function?
    f X (x) = 1/C; for: 0 <= x <= 7
    Hint: Find the numerical value of C


    2. Consider the probability density function given by:
    P X (x) = lambda/2; for: 0<= x <=2
    P X (x) = (1 - lambda)/4; for: 2<= x <=6

    This is a mixture of two uniform distributions. a)Sketch P X (x) for lambda=0.5. b) Sketch P X (x) for lambda=0.333. c) In a random sample from P X (x), 60% of the values were between 0 and 2. What would be an estimate for the value of lambda?
    \int_0^2 \frac{\lambda}{2} \, dx = 0.6 \Rightarrow \lambda = 0.6.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Mar 2008
    Posts
    18
    thank you guys
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 15th 2012, 11:37 PM
  2. exponential random variable with a random mean?
    Posted in the Advanced Statistics Forum
    Replies: 2
    Last Post: March 21st 2010, 03:05 PM
  3. Replies: 9
    Last Post: January 28th 2010, 08:26 AM
  4. Replies: 3
    Last Post: January 13th 2010, 11:44 AM
  5. random variable X and random variable X^2
    Posted in the Advanced Statistics Forum
    Replies: 13
    Last Post: April 24th 2008, 08:31 AM

Search Tags


/mathhelpforum @mathhelpforum