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  1. #1
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    help geo

    the random variable t can take any values and has a geometric distribution. it is given that p(t=1 or 2)= 0.4375. Find the value of p(t=1)


    thanks
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  2. #2
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    Quote Originally Posted by gracey View Post
    the random variable t can take any values and has a geometric distribution. it is given that p(t=1 or 2)= 0.4375. Find the value of p(t=1)


    thanks
    Good question:

    I am using this function as my pdf: f(t) = q^{t-1}p \Rightarrow (1-p)^{t-1}p where t is the number of trials.

    P(t=1 or t=2) = P(t=1) + P(t=2) \Rightarrow p + qp = p+(1-p)p \Rightarrow 2p-p^2 = .4375

    p^2-2p+.4375=0

    p=\frac{2 \pm \sqrt{4-1.75}}{2} \Rightarrow \frac{2 \pm 1.5}{2} = 0.25

    P(t=1) = p \Rightarrow 0.25
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