3. In an experiment, independent Bernoulli trials with success probability p were conducted until a success was observed

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3 In An Experiment Independent Bernoulli Trials With Success Probability P Were Conducted Until A Success Was Observed 1 (50.58 KiB) Viewed 29 times

3. In an experiment, independent Bernoulli trials with success probability p were conducted until a success was observed. In five independent repetitions of the experiment, the number of trials until the first success was recorded with the following results: 3, 2, 6, 4, 3. (a) Show that the log likelihood function can be written as 1p) 13log((1-P)) + 5log(P) Use this expression to derive the maximum likelihood estimator of the parameter p, the probability of success in an individual trial. [13 marks] (b) Construct an appropriate graph to illustrate how the maximum likelihood estimator is found from the likelihood function. Include labels on both of the axes. [7 marks] (20 marks)