A program will be run with 25 different sets of input. Let θ stand for the probability that an execution error will occur during a single run. We believe that, conditional on θ, each run of the program will encounter an error with probability θ and that the different runs are independent. Prior to running the program, we believe that θ has the uniform distribution on the interval [0, 1]. Suppose that we get errors during 10 of the 25 runs.
a. Find the posterior distribution of θ.
b. If we wanted to estimate θ by using squared error loss, what would our estimate be? |

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