We are testing a set of light bulbs from the same manufacturer, and each light bulb has the same probability of p to pass the test. We test 5 light bulbs and find that only the first 3 bulbs pass the test (represented as the observation D). What is the most likely value of p based on MLE? Complete the following derivation. The likelihood function that describes P(DP) is (Hint: the answer is a function of p) L(P) = P(Dp) =
Therefore, the log-likelihood function is: (Hint: the answer is a function of p) log L(P) = Maximizing the log-likelihood, we obtain PMLE = (write down a real number rounded to 2 decimal places in the format of XXX or - X.XX). Enter your answer here