Consider a series of independent Bernoulli Trials with a common probability of success π. Suppose we are interested in the number of failures Y before the first success. Note that Y is a random variable (0≤Y<[infinity]) that has the probability distribution function (PDF), Pr(Y∣π)=(1−π)ʸπ.
In an experiment conducted in n=15 trials, we observed following yᵢ values i=1,…,15, from Pr(yᵢ∣π)=(1−π)ʸⁱπ y=(0,9,5,7,2,11,1,8,6,8,3,9,0,8,5)
Write down the log-likelihood function for y=(y₁,…,yₙ),n=15 independent observations.