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Suppose there are two experiments. Experiments 1 has m outcomes and experiment 2 has n outcomes then the total
outcomes of both the experiment are m*n.
If r experiments are to be performed and there are n1 outcomes for the first experiment and
IE 322: Probabilistic Models in Industrial Engineering
Ethan Xingyuan Fang
January 2017
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Outline
1 Random Variable
2 Discrete Distributions
3 Expectation
4 Conditional Distribution
5 Joint Distribution
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Random Variable
What is a random variabl
IE322: Probabilistic Models in Industrial Engineering
Midterm 2 Formula Sheet, Fall 2016
Formula Sheet
V ar[X] = E[X 2 ] (E[X])2
Cov(X, Y ) = E[XY ] E[X]E[Y ]
V ar[aX + bY + c] = a2 V ar[X] + b2 V ar[Y ] + 2abCov[X, Y ]
Cov(aX + bY + e, cX + dY + f ) = ac
IE322: Probabilistic Models in Industrial Engineering
Final Exam Formula Sheet, Fall 2016
Formula Sheet
X P oisson() :
P (X = k) =
k e
k! ,
k = 0, 1, 2, .
X Binomial(n, p) : P (X = k) = Cn,k pk (1 p)nk =
E[X] = np, V ar[X] = np(1 p)
E[X] = ,
n!
k
k!(nk)!
IE322: Probabilistic Models in Industrial Engineering
Final Exam Practice, Fall 2016.
1. Suppose that there are two cafe clerks in Starbucks working to serve customers, and their
service times are independent and distributed as exponential of mean 2 and 2
IE322: Probabilistic Models in Industrial Engineering
Group Study - Week 15
November 28 - December 2, 2016
Problem 1. Suppose that the length of time that a patient wait in a doctors office before
receiving treatment is a random variable with mean 10 minu