Our class has 21 students of which 9 are Civil Engineering majors. Suppose I nee

Question

Our class has 21 students of which 9 are Civil Engineering majors. Suppose I need to randomly select one student per day from this class to have lunch with me. (a) Assume that I require five different students from Monday to Friday. Let X be the number of students of the sample of 5 that are Civil Engineering majors. What is the appropriate random variable to model X? What is E(X)? (b) Assume that I do not require five different students. Same student can go on different days. Let Y be the number of times from Monday to Friday that I have lunch with Civil Engineering majors. What is the appropriate random variable to model Y? What is E(Y)?

Explanation / Answer

In this example information given is as follows:

M = Number of students of Civil Engineering as Major = 9

N = Sample size =5

Under the assumption of different students each day,

Define random variable X : Number of students out of 5 with civil engineering as major.

Here due to underlying assumption, X will follow Hypergeometric Distribution

X ~ HypGeo (N=21, M=9, n=5)

The E(X) = nM/N = 5*9/21 = 2.14 nearly 2.

Y : Number of students out of 5 with civil engineering as major.

Then Y will follow Binomial Distribution

Y ~ B(n=5, p=9/21)

Then E(Y) = n*p = 5*9/21 = 2.14 nearly 2

Thus in both situation expected number of civil engineering major with whom teacher can dine is same.

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