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Math Help - Probability and median

  1. #1
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    Probability and median

    1) Suppose that Y has a Poisson distribution with mean=0. Compute Pr(Y>=1)

    2)Consider the random variable Y=1/X where X is uniform into (0,1).What is the median of Y?
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  2. #2
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    Quote Originally Posted by thandu3 View Post
    1) Suppose that Y has a Poisson distribution with mean=0. Compute Pr(Y>=1)

    Mr F says: Calculate 1 - Pr(Y = 0).

    2)Consider the random variable Y=1/X where X is uniform into (0,1).What is the median of Y?
    2) The cdf of Y is F(y) = \Pr\left( Y < y\right) = \Pr\left( \frac{1}{X} < y\right) = \Pr\left(X > \frac{1}{y}\right) = \int_{1/y}^1 dx = 1 - \frac{1}{y}.

    If m is the median of Y then F(m) = \frac{1}{2} \Rightarrow 1 - \frac{1}{m} = \frac{1}{2} \, ....
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    thanks

    thank you very much for your kind reply.
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