Question

Problem 2: The table provides the probability distribution for X the number of courses taught b at all degree-granting institutions of higher learning in the United States during the Fall 2017 semester # of courses taught by faculty 0.23 0.34 0.24 0.12 0.07 Given a randomly selected faculty member teaches at least 2 courses during the Fall semester, what is the probability they teach exactly 4 courses? a. b. What is the expected number of courses taught by a faculty member during the Fall 2017 semester? courses symbol value 1IPage

Answer 1

Here we want to find P(X = 4 | X >= 2) .

0.12 0.12 P(X = 4) P(X > 2) 0.340.240.120.07 0.77

12 0.155844

So answer of part a) is 0.155844

b) Here we want to find E(X)

The formula of expectation of X is as follows:

E(X)-〉 X * p(2)

Let's make table in excel:

p(x) X*p(x) 0.23 0.34 0.24 0.12 0.07 0.23 0.68 0.72 0.48 0.35 2.46 This is the expected value of X. 3 4 4 5 8

The formulae used on the above excel-sheet are as follows:

p(x) 0.23 0.34 0.24 0.12 0.07 X*p(x) A2* B2 A4 B4 A5*B5 4 3 -SUM(C2:C6) This is the expected

S0 answer of part b) is 2.46