Question

i need the answer to 6-c

5. A professor has a large class. The proportion of students who miss an assignment is a beta distribution with parameters with α and β 2. (a) Determine the probability that at least 70% of the students will miss an assignment. 6. Using the distribution given in problem 5 (b) What is the expected proportion of missed assignments? (c) What is the variance of this distribution?

Answer 1

5)Given that the proportion of the students who miss an assignment is
~Beta (o = 4,3=2)
.

a) The probability,

P(X 0.7)-1- P(X < 0.7) P(X > 0.7)-1 pBeta (0.7,a 4,B-2) P(X 0.7) 0.4718

Use the following R command:

> 1-pbeta(0.7, shape1=4, shape2=2)
[1] 0.47178

6)

b)The mean of the Beta distribution is

$E(X)=\frac{\alpha }{\alpha +\beta }=\frac{4}{4+2}={\color{Blue} 0.6667}$

c)The variance of the Beta distribution is

$Var(X)=\frac{\alpha \beta }{\left (\alpha +\beta \right ) ^2\left (\alpha +\beta +1 \right )}=\frac{4 \times 2}{(4+2)^2(4+2+1)}={\color{Blue} 0.0317}$​​​​​​​