I have some conceptual hiccups ( for a lack of better word ) with beta Random variables.
Here's the question:
The number of students who get failing grade in a hard test is given by Beta B(2,3) random variable.
α = 2, β= 3
To determine the number of students that fail, I found the Mode using the formula Mode = (α−1)/(α+β−2)
I get (2-1)/(2+3-2) = 1/3
Therefore, the number of students that fail is 1/3rd.
Is this right?
Now how do I find the the probability of 80% students passing the test?