1. Not finding help here? Sign up for a free 30min tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Small Poisson Question

  1. Dec 5, 2006 #1
    Hello

    I just found this forum, was recommended it by a person that I know and have a small probability question regarding Poisson distribution.

    Let (T,U) be a to dimensional discrete stochastic vector with the probability function [tex]p_{T,U} [/tex] given by.

    [tex]P(T=t, U = u) = \left{ \begin{array}{cccc} \frac{1}{3} \cdot e^{-\lambda} \frac{\lambda^u}{u!} & u \in \{-1,0,1\} & \mathrm{and} & t \in \{0, 1, \ldots\} \\0 & \mathrm{elsewhere.} \end{array} [/tex]

    where [tex]\lambda > 0 [/tex]

    1)

    describe the support for [tex]\mathrm{supp} (P_{T,U}) [/tex]

    Solution (1) the support [tex]\mathrm{supp} (P_{T,U}) [/tex] is the set of values for the real valued probability function P which produces non-negative values. therefore [tex]\mathrm{supp} (P_{T,U}) = \{0,1, \ldots \} [/tex]

    2)

    show that the probability function [tex]p_T [/tex] and [tex]p_U [/tex] for T and U is.

    [tex]P(T = t) = P_{T} = \left{ \begin{array}{cccc} \frac{1}{3} & t \in \{-1,0,1\} \\0 & \mathrm{elsewhere.} \end{array} [/tex]

    and

    [tex]P(U = u) = P_{U} = \left{ \begin{array}{cccc} e^{-\lambda} \frac{\lambda^{u}}{u!} & u \in \{0,1,\ldots\} \\0 & \mathrm{elsewhere.} \end{array} [/tex]

    which inturn means [tex]U \sim po(\lambda) [/tex]

    Solution (2)

    How do I show this ? If not as above. Or do I show that they have same variance??


    (3) Assume that [tex]\lambda = 1 [/tex] then [tex]P(T=U) = \frac{2}{3} e^{-\lambda} [/tex]


    Solution is [tex]P(T = U) = P(t \cup u)[/tex]???


    Best Regards
    Hartogsohn
     
  2. jcsd
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Can you help with the solution or looking for help too?



Similar Discussions: Small Poisson Question
  1. PDE question (Replies: 0)

  2. 1st order ODE Question (Replies: 0)

  3. Game Theory question (Replies: 0)

  4. Probability question (Replies: 0)

Loading...