This function involves the parameter , given the data (the and ). The discrete data and the pny statistic (a count or summation) are known. The likelihood function is not a probability y function; but it is a positive function and 01. The left hand side is read “the likelihood of p the parameter , given and . pnyLikelihood theoryand the likelihood functionare fundamentalin the statisticalsciences.
Note the similarity between the probability function and the likelihood function; the right hand sides are the same. The difference between the two functions is the conditioning of the left hand sides. The probability function returns probabilities of the data, given the sample size and the parameters, while the likelihood function gives the relative likelihoods for different values of the parameter, given the sample size and the data.