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Math Help - Conditional expected value

  1. #1
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    Conditional expected value

    There's a mouse and three doors:

    The first door takes the mouse to a cheese in 3 minutes.
    The second door takes the mouse to the initial state (he has to choose a door again) in 5 minutes.
    The third door takes the mouse to the initial state in 5 minutes.

    Always the mouse chooses a door randomly and independient.
    What's the expected value of the time the mouse takes to get the cheese?

    i would really apreacciate a help here
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  2. #2
    MHF Contributor harish21's Avatar
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    Re: Conditional expected value

    The probability of the mouse going into any of the rooms is 1/3.

    denote your 3 rooms by i = 1,2,3 and the starting(initial) point by i=0.

    let E(i) be the expected time till the mouse finds cheese if it has arrived at i.

    now set up your equations as:


     E(0) = \frac{1}{3} E(1) + \frac{1}{3} E(2) + \frac{1}{3} E(3)

    E(1) = 3

    E(2)=??

    E(3)=??

    try to figure out your equations for E(2) and E(3) and using the four equations, you can find E(0)
    Last edited by harish21; April 21st 2012 at 08:00 AM.
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  3. #3
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    Re: Conditional expected value

    oh! thank you! you are ideas generator machine

    E(2) = 5 + E(X)
    E(3) = 5+ E(X)

    GREAT!
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  4. #4
    MHF Contributor harish21's Avatar
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    Re: Conditional expected value

    Quote Originally Posted by FRMST View Post
    oh! thank you! you are ideas generator machine

    E(2) = 5 + E(X)
    E(3) = 5+ E(X)

    GREAT!
    it should be 5+E(0)
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