A scientist needs to estimate the mean time between aftershocks of an earthquake. Observational data from 5 aftershocks gives waiting times of 5, 7.2, 4.3, 6.6, and 4.5 hours. Assuming the waiting time for all of the aftershocks follows an Exponential distribution with the same rate parameter λ, what is the Maximum Likelihood Estimate for the mean length of time between aftershocks? What property of the Maximum Likelihood Estimator do you need to appeal to in order to make this calculation? A vendor of seeds has purchased a stock of seeds of an exotic flower, and wants to estimate the probability that one of these seeds germinates. Therefore, she plants 5 seeds in each of 3 large pots. After one month, she finds that the number of germinating seeds in the first, second and third pot were, respectively, 2, 3 and 2. Assuming that the number of germinating seeds in each of the pots follows a Binomial distribution with the same probability p of success (that is, germination), compute the Maximum Likelihood estimator for the probability that a seed germinates, using the formula that you derived above.
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A scientist needs to estimate the
mean time between aftershocks of an earthquake. Observational data from 5 aftershocks gives waiting times of 5, 7.2, 4.3, 6.6, and 4.5 hours. Assuming the waiting time for all of the aftershocks follows an Exponential distribution with the same rate parameter λ, what is the Maximum Likelihood Estimate for the mean length of time between aftershocks? What property of the Maximum Likelihood Estimator do you need to appeal to in order to make this calculation? -
A vendor of seeds has purchased a stock of seeds of an exotic flower, and wants to estimate the probability that one of these seeds germinates. Therefore, she plants 5 seeds in each of 3 large pots. After one month, she finds that the number of germinating seeds in the first, second and third pot were, respectively, 2, 3 and 2. Assuming that the number of germinating seeds in each of the pots follows a Binomial distribution with the same probability p of success (that is, germination), compute the Maximum Likelihood estimator for the probability that a seed germinates, using the formula that you derived above.
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