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## Main Question or Discussion Point

Dear All,

The bivariate Poisson distribution is as follows,

[tex]

\[ f(y_{s},y_{t})=e^{-(\theta_{s} + \theta_{t}+\theta_{st})}\frac{\theta_{s}^{y_{s}}}{y_{s}!}\frac{\theta_{t}^{y_{t}}}{y_{t}!}

\sum_{k=0}^{min(y_{s},y_{t})} \binom{y_{s}}{k} \binom{y_{t}}{k} k!\left(\frac{\theta_{st}}{\theta_{s} \theta_{t}}\right)^k.\]

[/tex]

Given that [tex] f(y_{s},y_{t}) >= 0 [/tex], solve for [tex] \theta_{st} [/tex].

Many thanks in advance,

George

The bivariate Poisson distribution is as follows,

[tex]

\[ f(y_{s},y_{t})=e^{-(\theta_{s} + \theta_{t}+\theta_{st})}\frac{\theta_{s}^{y_{s}}}{y_{s}!}\frac{\theta_{t}^{y_{t}}}{y_{t}!}

\sum_{k=0}^{min(y_{s},y_{t})} \binom{y_{s}}{k} \binom{y_{t}}{k} k!\left(\frac{\theta_{st}}{\theta_{s} \theta_{t}}\right)^k.\]

[/tex]

Given that [tex] f(y_{s},y_{t}) >= 0 [/tex], solve for [tex] \theta_{st} [/tex].

Many thanks in advance,

George

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