I'm doing revisions for Statistics and came across this question that I can't tackle. Bayesian is the worst topic for me because I can't seem to understand it. I hope you guys can help me out!
Records collected over many years show that on average 74% of first year students have IQ's of at least 155. Of course, the percentage 100 x theta varies from year to year and this variation is measured by a standard deviation of 3%. Suppose that the proportion of theta has a beta distribution. A sample of 30 first year students enrolling in 2007 showed that only 18 of them have IQ's of at least 115.
What is the prior estimate of theta in 2007?
What is the maximum likelihood estimate of theta in 2007?
Determine the mean of the posterior distribution of theta in 2007.
Some help please!