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The chance of heads of a random coin is picked according to the beta (1,1) distribution. For each part, you must show work or reference a relevant section of the textbook.
a) Find P(first toss is heads).
b) Find P(first toss is heads, second toss is tails).
c) Compare your answer in part b to the chance of {first toss is heads, second toss is tails} {first toss is heads, second toss is tails} given that you are tossing a fair coin twice. Is it larger or smaller? Give an intuitive explanation.
d) Find the posterior density of the chance of heads given that you've seen one head and one tail.
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