Results 1 to 3 of 3

Math Help - Problem Asking to Determine the Variance of a Random Variable: Unable to Locate Error

  1. #1
    Junior Member
    Joined
    Apr 2011
    Posts
    43

    Problem Asking to Determine the Variance of a Random Variable: Unable to Locate Error

    Hello,
    I am solving the following problem: A Salesman has scheduled two appointments to sell encyclopedias. His first appointment will lead to a sale with probability .3, and his second will lead independently to a sale with probability .6. Any sale made is equally likely to be either for the deluxe model, which costs $1000, or the standard model which costs $500. Determine the probability mass function of X, the total dollar value of all sales and determine the mean and variance of X.
    I solved:
    1. P(X=0) = 0.28
    2. P(X=500) = 0.27
    3. P( X=1000) = 0.315
    4. P( X=1500)= 0.09
    5. P(X=2000)= 0.045
    E[X] = $675, since 0(0.28) + 0.27(500) + (0.315)(1000) + 0.09(1500) + 0.045(2000) = $675
    Var[X] = E[X2] (E[X])^2
    E[X2] = 0.28^2(0) + 0.27^2(500) + 0.315^2(1000) + 0.09^2(1500) + 0.045^2(2000) = 151.875
    So, Var[X] = 151.875 (675^2) = A ridiculously low negative number.
    Obviously this is incorrect, or at least I think it is.
    Could someone please tell me where my error lies?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member MaxJasper's Avatar
    Joined
    Aug 2012
    From
    Canada
    Posts
    482
    Thanks
    54

    Lightbulb Re: Problem Asking to Determine the Variance of a Random Variable: Unable to Locate E

    Assuming a normal distribution:
    Attached Thumbnails Attached Thumbnails Problem Asking to Determine the Variance of a Random Variable: Unable to Locate Error-probability-encyclopedia-sales.png  
    Last edited by MaxJasper; October 2nd 2012 at 09:42 AM.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Sep 2012
    From
    Due North
    Posts
    26

    Re: Problem Asking to Determine the Variance of a Random Variable: Unable to Locate E

    Hi, I didn't check the probabilities but this looks wrong since you are never going to be squaring probabilities but rather the various events of X:
    E[X2] = 0.28^2(0) + 0.27^2(500) + 0.315^2(1000) + 0.09^2(1500) + 0.045^2(2000) = 151.875
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 1
    Last Post: October 15th 2012, 10:37 PM
  2. Replies: 2
    Last Post: May 6th 2012, 12:49 PM
  3. normal random variable with zero variance
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 16th 2012, 03:49 AM
  4. random variable, mean, variance
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: April 25th 2009, 01:30 AM
  5. Mean/variance of random variable...hmmmm
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: April 11th 2008, 04:47 PM

Search Tags


/mathhelpforum @mathhelpforum