# Log likelihood for Joint distribution function

I have two different distributions such as $x_1,\ldots,x_6$ are independent and identically distributed. Poisson observations with mean lambda, and $y_1,\ldots,y_8$ are independent and identically distributed $\mathcal{N}(\ln(\lambda),1)$. If $x_1+\ldots+x_6 = 8$ and $y_1+\ldots+y_8=16$ I would like to write down the $\log$-likelihood function. Please pay attention to this question. Thanks in advance.

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 If the data are independent then the likelihood is just the product of the likelihoods for each datum value. – Stéphane Laurent Oct 21 '12 at 13:28