Mathematics
Mathematics, 18.03.2020 06:14, Irvin2284

You want to estimate the probability that a lightbulb of a famous brand will last more than 6.500 hours. You choose 10,000 bulbs randomly and observe that 9,580 did last more than 6,500 while the rest did not.

a. Write down the likelihood function to estimate this probability. Be specific with the number of positive test results in the function. (4 points)
b. What is the value of the maximum likelihood estimate of the probability? (4 points)
c. What is the likelihood of observing this experiment outcome when the true probability is 98%? (4 points)
d. What is the method of moments estimate? (4 points)
e. Argue whether the following statement is true or false: In general, the method of moments estimate is always equal to maximum likelihood estimate. (4 points)

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