Question

Three students scheduled interviews for summer employment at the Brookwood Institute. In each case the interview results in either an offer for a position or no offer. Experimental outcomes are defined in terms of the results of the three interviews.

Required:
a. List the experimental outcomes.
b. Define a random variable that represents the number of offers made. Is the random variable continuous?
c. Show the value of the random variable for each of the experimental outcomes.

Answer 1

a. OOO, OON, ONO, NOO, ONN, NON, NNO, NNN

b. No, the variable is discrete.

c. x(OOO) = 3; x(OON) = 2; x(ONO) = 2; x(NOO) = 2; x(ONN) = 1; x(NON) = 1; x(NNO) = 1; x(NNN) = 0

Explanation:

Let 'O' represent an offer and 'N' represent a no offer.

a. The experimental outcomes are:

OOO, OON, ONO, NOO, ONN, NON, NNO, NNN

b. Let x be the number of offer mades (number of 'O's), it can only assume the values of 1, 2 or 3, and therefore is not continuous, it is a discrete random variable.

c. The values of x for each outcome are:

x(OOO) = 3;

x(OON) = 2;

x(ONO) = 2;

x(NOO) = 2;

x(ONN) = 1;

x(NON) = 1;

x(NNO) = 1;

x(NNN) = 0