Kernel: Python 2
ATMS 391 Homework 11
Problem 1
Assume that you have a hypothetical situation in which it is claimed that the climatological probability of a cloudless day in winter is 6/7, after observing x = 15 cloudless days on N = 25 independent occasions. Assume that the prior distribution can be approximated by a Beta distrubution with 4.
(a) Generate the Posterior distribution using Bayes' theorem.
In [13]:
(b) What is the mean of the posterior distribution?
In [14]:
Posterior Mean: 0.575757575758
(c) What are the 95% confidence intervals of the Posterior?
In [23]:
[7.5531402197569343e-22, 4.5411267644511275]
(d) What is the probability that the original claim is correct? (Hint: Evaluate the sum of the posterior above the probability 6/7)
In [19]:
6.9691911785028847e-05
Problem 2
Run Exercise 4, we will talk about it next Tuesday!!
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