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.

A First Course in Probability (10th Edition)
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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
¹(1-x) ³-¹,
f(x) =
I(a + B)
r(a)r(3)"
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.
Transcribed Image Text: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 ¹(1-x) ³-¹, f(x) = I(a + B) r(a)r(3)" 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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