Chapter 2: Discrete Random Variables
2.1 Denitions
Recall that an experiment consists of a procedure and observations. In this chapter, we begin to examine probability models that assign numbers to outcomes in the sample space S . When we observe one of t

IEN310 Chapter 6: Problems
6.1.2 6.1.3 6.1.4 6.1.5 6.2.1 (very hard) 6.2.3 6.4.4 6.4.6 6.6.1 6.6.2 (the answer to part b should read The standard deviation of K100 = and not Var[K100] = 6.7.1
IEN310 Chapter 6: Solutions

Chapter 5: Random Vectors
5. Introduction
The denitions and theorems in Chapter 4 concerning probability models of two random variables X and Y can be generalized to experiments that yield an arbitrary number of random variables X1 , . . . , Xn . Vector n

Chapter 4: Pairs of Random Variables
4. Introduction
This chapter analyzes experiments that produce two random variables, X and Y . The probability model for such an experiment contains the properties of the individual random variables and it also contain

IEN310 Chapter 4: Problems
4.1.1 4.1.3 4.2.1 4.2.4 4.2.7 (The solutions should read: and therefore we know that the k = k n 1 rejections must have occurred.) 4.3.1 4.4.1 (In equation 3 of the solutions f X ,Y ( x, y ) should be 2 dy dx and not dy dx.) 4.4

Chapter 3: Continuous Random Variables
3. The Continuous Sample Space
Continuous random variables range over continuous sets of numbers, which are sometimes referred to as intervals. An interval contains all of the real numbers between two limits. For the

IEN310 Chapter 3: Problems
3.1.1 3.1.2 3.2.4 3.3.2 3.4.3 3.4.4 3.4.9 3.5.5 3.5.7 (The solution to part (a) could have been expressed as 84 70 70 84 = due to symmetry.) P[ H 84] = 1 X X 3.6.2 3.6.3 3.6.4 3.6.7 (For FT(t) = 0, t < 0 (not t < -1). 3.7.1 3.7.

IEN310 Chapter 2: Problems
2.2.3 2.2.5 2.2.6 2.2.7 2.3.4 2.3.7 2.3.10 2.3.12 (part c and part d solutions are in error) 2.4.3 2.4.7 2.5.7 2.6.3 2.7.7 2.8.5 2.9.3
IEN310 Chapter 2: Problem Solutions

IEN 310 Lecture Notes Introduction to Engineering Probability Professor J. Sharit University of Miami
Spring 2009
Chapter 1: Experiments, Models, and Probabilities
1. Introduction to the Concept of Probability
We generally accept as a given that the proba

Chapter 6: Sums of Random Variables
6. Introduction
There are many applications of probability theory in which random variables of the form Wn = X1 + Xn appear. Our goal is to derive the n-dimensional probability model of Wn . First, we will consider expe