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Math Help - Geometric distribution problem

  1. #1
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    Geometric distribution problem

    Question:
    If Y has a geometric distribution with success probability .3, what is the largest value, y0, such
    that P(Y > y0) ≥ .1?

    Attempt:
    So i represented the probability of the random variable as a summation

    once working with the other end =>

    summation from y0 =0 to y0-1 of q^y0-1 p < 0.9

    with the change of variables l= y0-1

    summation from l=0 to l of q^l p < 0.9

    now finding the partial sum of the geometric series

    p/(1-q) < 0.9
    0.3/ 0.3 < 0.9

    i'm stuck here ? how do i get the value for y0 ?
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  2. #2
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    Quote Originally Posted by electricalphysics View Post
    Question:
    If Y has a geometric distribution with success probability .3, what is the largest value, y0, such
    that P(Y > y0) ≥ .1?

    Attempt:
    So i represented the probability of the random variable as a summation

    once working with the other end =>

    summation from y0 =0 to y0-1 of q^y0-1 p < 0.9

    with the change of variables l= y0-1

    summation from l=0 to l of q^l p < 0.9

    now finding the partial sum of the geometric series

    p/(1-q) < 0.9
    0.3/ 0.3 < 0.9

    i'm stuck here ? how do i get the value for y0 ?
    \Pr(Y > y_0) \geq 0.1 \Rightarrow 1 - \Pr(Y \leq y_0) \geq 0.1 \Rightarrow \Pr(Y \leq y_0) < 0.9 \Rightarrow (0.7)^{y_0} > 0.1 (see cdf given here Geometric distribution - Wikipedia, the free encyclopedia).

    So your job is to find the largest integer solution to 0.7^{y_0} > 0.1. I suggest using trial and error as an effective approach.
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