Suppose I flip a coin 10 times and get 7 heads - based on a Binomial Distribution, I can create a Likelihood Function and estimate the probability of getting a head is 0.7.
Now, suppose someone tells me that they have very strong evidence to believe that the probability of getting a head is 0.9. Suppose I decide to use a Beta Distribution(alpha, beta) as a prior.
My Question: I know that the Expected Value of the Beta Distribution is 'alpha/(alpha + beta)'. If I want to use the Prior Information that was provided to me - does this mean that I have choose values of 'alpha and beta' such that 'alpha/(alpha+beta)' = 0.9? For example - based on the n = 10 samples I observed, in this case, would alpha = 9 and beta = 1?