I am trying to use Yale stock market crash confidence indice to make a crash probability estimate. The Crash Confidence Index is the percentage of respondents who think that the probability of a crash is less than 10%. given a indice of 35.58%, I used Excel Solver to find the value of "a" to get beta cumulative probability of 35.58%, while X=10% and b=1-a. Thus, the mean of beta distribution (or simply value of "a" since I said b=1-a) is the expected probability of stock market crash based on what the respondents think. Is that my solution sensible? any suggestion of this or another solution?