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enter image description here

I don't understand why my answer is wrong. My understand of likelihood is the P ( Data | model). For example, if the model is that a coin is fair, and the coin was flipped 10 times and came up heads 6 times, then the likelihood is (some binomial distribution math goes here... unsure what it is actually... I think it's $6 choose 10 * 0.5 ^ 6 * 0.5 ^ 4$. Is that right?)

  1. You go to Las Vegas and sit down at a slot machine. You are told by a highly reliable source that, for each spin, the probability of hitting the jackpot is either 1 in 1,000 or 1 in 1,000,000, but you have no prior information to tell you which of the two it is. You play ten times, but do not win the jackpot. What is the posterior probability that the true odds of hitting the jackpot are 1 in 1,000?

So is the math going to be:

$\frac{true-positive}{true-positive + false-positive}$

$\frac{(\frac{999}{1000}) ^{10} * \frac{1}{1000}}{(\frac{999}{1000}) ^{10} * \frac{1}{1000} + (\frac{999999}{1000000}) ^{10}}$

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Are you sure the first question is on Bayes theorem? Did you attach the wrong screenshot? Maybe i'm just not understanding it

This is what I get as the answer for the second question. The prior likelihood for each of the two is 50% to start. Then multiply each of them by the likelihood to fail 10 times (999/1000 or 999999/1000000) Then normalize

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  • $\begingroup$ What is normalizing? $\endgroup$ – Jwan622 Jun 5 '17 at 13:17
  • $\begingroup$ if you sum up the posterior values they are less than one. (that sum happens to represent your prior belief that you would miss winning the jackpot in 10 trials). However after the 10 trials you know that you did miss it 10 times. So afterwards, the odds that you would miss 10 times needs to sum to 1 (100%) so you divide each of the individual posteriors by the sum of the two posteriors to get values that sum to 1.0, but have the same ratio between them as they did before they summed to 1.0 $\endgroup$ – Fairly Nerdy Jun 6 '17 at 2:36
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For the first problem, unless you are in a Bayesian course, we think that parameters are unknown fixed quantities and they don't have a 'distribution'. So I guess the answer is the last one.

P.S. This problem is not designed properly because you might understand this but fails to catch what the professor wants to test you. In an epidemiology test I met multiple choice problem like "To monitor effects of an assigned exposure which one is the best" with choices such as 'cohort' and 'experimental' and I was deeply confused. Later I realized that this is a stupid English problem because of the word 'assigned'.

You don't need to do stupid conceptual problem right to understand the concept of statistics, let alone to practice it.

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