2019-01-14[Stay Sharp]likelihood function

What is likelihood function ?

I like the answer on stackexchange, the author said,

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likelihood function is a function of the parameters of a statistical model, it describes the plausibility of a parameter value of the statistical model assumed to describe the observed data, given specific observed data. it's always defined as a function of

.
For discrete probability distribution,

the likelihood function of equals to the probability of given the value of `.

For continuous probability distribution,

the likelihood function of equals to the density function of given the value of .

References

https://stats.stackexchange.com/questions/2641/what-is-the-difference-between-likelihood-and-probability