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Math Help - probability (eating birds)

  1. #1
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    probability (eating birds)

    hello,I'm studying for an exam,and I need some help with this one:

    assume that the time units are discrete:

    there are 3 birds A B & C,at each time unit a bird can eat or guard,with probability 1/2 independently from the other birds,or her previous action.
    at each time unit a hawk arrives,and if there is not 1 guard at least ,he randomly eats one of the birds.

    a)if X is a random variable which counts the time it took for the hawk to eat all the 3 birds then E(X)=?
    b)if the hawk didn't eat bird A first then her expected life span is?

    help would be appreciated..thanks
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  2. #2
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    Quote Originally Posted by parallel View Post
    hello,I'm studying for an exam,and I need some help with this one:

    assume that the time units are discrete:

    there are 3 birds A B & C,at each time unit a bird can eat or guard,with probability 1/2 independently from the other birds,or her previous action.
    at each time unit a hawk arrives,and if there is not 1 guard at least ,he randomly eats one of the birds.

    a)if X is a random variable which counts the time it took for the hawk to eat all the 3 birds then E(X)=?
    b)if the hawk didn't eat bird A first then her expected life span is?

    help would be appreciated..thanks
    Here are some fill-in-the-blanks study questions intended to lead you to the answer for (a):
    1. The hawk eating the birds represent _________ trials with parameters (success probabilities) p1, p2 and p3 depending on the number of birds. The values for these parameters are ___, ___ and ___.
    2. The waiting time for a hawk to successfully eat a bird when there are k birds is a random variable Xk with a _________ distribution with parameter ___. The mean of this distribution is ___.
    3. The time X it takes to eat all three birds is the sum of the three random variables X1, X2 and X3. The mean of a sum of random variables equals ___ ___ __ ___ _____. So the mean of X is ___.
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  3. #3
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    that really helped,thanks alot

    it ends up to 16, right?

    any clue about (b)?
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  4. #4
    Junior Member frenzy's Avatar
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    Quote Originally Posted by parallel View Post
    that really helped,thanks alot

    it ends up to 16, right?

    ...
    hmm...I get 14
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  5. #5
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    yea it's 14 , 2+4+8=14 (I made a stupid mistake)
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