Suppose it is known that the proportion of students who get an A in a particular statistics course follows a beta distribution with a = 5 and 3 = 2, having probability density function f(x) = I(a + B) r(a)r(3) za ¹(1-x)³-¹, 0 < x < 1. (a) Find the probability that more than half of the students will get an A in this class this semester. (b) On average, what proportion of students are expected to get an A in this class this semester? If you know the form for the expected value for a Beta random variable, you do not need to reprove it.

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