Results 1 to 2 of 2

Math Help - Normal distribution with 2 equations

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    1

    Normal distribution with 2 equations

    Hi Guys,
    I'm having trouble with the following Question. I don't know where I should start and what I need to do with the correlation. I hope you can show me a direction to solve this:


    The Mayor wishes to build a new tunnel. He has been told that the cost (C) of the tunnel (in billions of dollars) can be estimated by:

    C = 1.5 + 0.4 T1

    where T1 is the time in years which it takes to build the tunnel. The Mayor has also been told that T1 is a random variable with a normal distribution with a mean of 3 and a standard deviation of 0.6.
    Opposition research shows that alternatively a new bridge could be built for cost B:

    B = 1.3 + 0.4 T2

    where T2 is the time in years which it takes to build the bridge. They have also been told that T2 is a random variable with a normal distribution with a mean of 2.5 and a standard deviation of 0.5.
    The times taken to build the tunnel and the bridge have a correlation of 0.8.
    What is the probability that the bridge would cost more to build than the tunnel?


    Cheers
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor matheagle's Avatar
    Joined
    Feb 2009
    Posts
    2,763
    Thanks
    5
    You want P(B-C>0)

    NOW B-C is a normal random variable.
    YOUR job is to compute it's mean and variance and calculate that probability above.
    I had thought that T1 and T2 would be independent, but they gave you the correlation.
    Hence you can compute the their covariance and thus the variance of B-C.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. normal distribution prior and posterior distribution proof
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: March 9th 2011, 07:12 PM
  2. Replies: 1
    Last Post: October 18th 2010, 02:41 PM
  3. Replies: 2
    Last Post: March 29th 2010, 03:05 PM
  4. Replies: 3
    Last Post: February 6th 2009, 04:59 AM
  5. Replies: 1
    Last Post: April 20th 2008, 07:35 PM

Search Tags


/mathhelpforum @mathhelpforum