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    Greetings, I was solving a probability exercise from a Stats pastpaper and I got stuck in 1 mark question.

    Erika is a birdwatcher. The probability that she will see a woodpecker on any given day is 1/8. It is assumed that this probability is unaffected by whether she has seen a woodpecker on any other day.

    i) Calculate the probability that Erika first sees a woodpecker

    (a) on the third day [3] - I got 49/512 which is right

    (b) after the third day [3] I got 343/512 which is right

    ii) Find the expectation of the number of days up to and including the first day on which she sees woodpecker [1]

    I don't know how to calculate E(X) without knowing how many times she will go. Or maybe they're asking for something else?
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    (Original post by Blackfyre)
    Greetings, I was solving a probability exercise from a Stats pastpaper and I got stuck in 1 mark question.

    Erika is a birdwatcher. The probability that she will see a woodpecker on any given day is 1/8. It is assumed that this probability is unaffected by whether she has seen a woodpecker on any other day.

    i) Calculate the probability that Erika first sees a woodpecker

    (a) on the third day [3] - I got 49/512 which is right

    (b) after the third day [3] I got 343/512 which is right

    ii) Find the expectation of the number of days up to and including the first day on which she sees woodpecker [1]

    I don't know how to calculate E(X) without knowing how many times she will go. Or maybe they're asking for something else?
    How did you work out a and b ?
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    (Original post by zed963)
    How did you work out a and b ?
    I used tree diagram for both.

    a) 7/8*7/8*1/8
    b) (7/8)^3
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    Bump, still need help.
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    (Original post by Blackfyre)
    Bump, still need help.
    \displaystyle E(X) =\sum_{x=1}^{\infty}\left(x    \times P(X=x)\right)


    \displaystyle\sum_{x=1}^{\infty}  \left(x \times\frac{1}{8}\times\left(   \frac{7}{8}   \right)^{x-1} \right)



    PS: You should recognise the distribution, in which case you may be able to just quote the result, rather than use first principles.
 
 
 
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