The indicator random variable I {A} associated with event A is
defined as
I{A} = 1 if A occurs ;
=0 if A does not occur
:
For each of the problem below find the expected value associated
with the problem using the known property of linearity of
Expectation, E[X+Y] = E[X] + E[Y], provided that X and Y are
indicator random variable for an event A occurring.
Problem 1
Given a dice with 6 faces, numbering from 1 to 6. Find the
probability of getting the number 5 when the dice is thrown.
Declare an indicator random variable for the event associated
to throwing the dice to get number 5 for n number of throws
Let X be the random variable to get number 5 in n number of
throws
What is the probability of getting the number 5 when dice is
thrown?
What is the expectation of getting the number 5 in one throw?
Show your working.
What is the expected value for getting number 5 in n number of
throws
Problem 2
Suppose that you need to hire a new office assistant. Your
previous attempts at hiring have been unsuccessful, and you decide
to use an employment agency. The employment agency sends you one
candidate each day. You interview that person and then decide
either to hire that person or not. You must pay the employment
agency a small fee to interview an applicant. To actually hire an
applicant is more costly, however, since you must fire your current
office assistant and pay a substantial hiring fee to the employment
agency. You are committed to having, at all times, the best
possible person for the job. Therefore, you decide that, after
interviewing each applicant, if that applicant is better qualified
than the current office assistant, you will fire the current office
assistant and hire the new applicant. You are willing to pay the
resulting price of this strategy, but you wish to estimate what
that price will be.
Write a pseudocode for the above problem.
Discuss step by step approach on how you would find the
estimated cost of hiring a candidate. Show your workings using
indicator random variable and expectation values.