# Constructing a discrete prior

Suppose American female college students are asked the following question: Do you feel that you are "underweight", "just right", or "overweight"?

Of the students who don't respond "just right", you can denote the proportion of women who believe they're overweight with P. The value of P is unknown, but you can construct a probability distribution which reflects your beliefs about its value!

The following table displays prior distributions for three people: Sean, Madison, and Kevin. Each person believes values for P of 0.5, 0.6, 0.7, 0.8, and 0.9 are plausible, but they assign different probabilities to each:

    P Sean_Prior Madison_Prior Kevin_Prior
1 0.5        0.2           0.3         0.1
2 0.6        0.2           0.3         0.1
3 0.7        0.2           0.2         0.2
4 0.8        0.2           0.1         0.3
5 0.9        0.2           0.1         0.3


Which person thinks the proportion of women students believing they are overweight is relatively high?