How to calculate weighted negative log-likelihood?

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I'm calculating the negative log-likelihood for a bunch of tasks:
NLL = p1∗p2∗...∗pn = −(log(p1)+...+log(pn))
p is the probability of a task. The tasks appear at a certain time point and I want to give to the newer tasks a higher weight (influence).
If I have weights for each task (i.e. n weights), how can I calculate the weighted NLL?

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