Math 110 - Chapter 5,6,7,8,9 Terms with more than 115 correct answers.
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Math
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Math
Math 110 - Chapter 5,6,7,8,9 Terms with more than 115 correct answers.
Math 110 - Chapter 5,6,7,8,9 Terms with more than 115 correct answers.
Math 110 - Chapter 5,6,7,8,9 Terms with more than 115 correct answers.
Math 110 - Chapter 5,6,7,8,9 Terms with more than 115 correct answers.
Math 110 - ...
Math 110 - Chapter 5,6,7,8,9 Terms with
more than 115 correct answers.
Math 110 - Chapter 5,6,7,8,9 Terms with
more than 115 correct answers.
Routing Problems - ANSWER- problems concerned with routing the delivery of good to
services to a set of destinations
Street-Routing Problems - ANSWER- problems where a specified set of connections
(roads, bridges, edges) must be traveled at least once
Vertex Set - ANSWER- the set of vertices of a graph
Edge List - ANSWER- a list of all the edges of a graph
Adjacent Vertices - ANSWER- two vertices connected by an edge
Loop - ANSWER- an edge that connects a vertex with itself
Multiple Edges - ANSWER- two or more edges connecting the two same vertices
Degree - ANSWER- number of edges meeting at the vertex
Odd (Even) Vertex - ANSWER- a vertex of odd (even) degree
Clique - ANSWER- a set of vertices with the property that any two are adjacent
Simple Graph - ANSWER- a graph with no loops or multiple edges
Isolated Vertex - ANSWER- a vertex of degree 0
Adjacent Edges - ANSWER- two edges with a shared vertex
Path - ANSWER- a sequence of edges each adjacent to the next, with no edge included
more than once, and starting and ending at different vertices
Circuit - ANSWER- same as a path but starting and ending at the same vertex
Length - ANSWER- number of edges in a path or a circuit
Euler Path - ANSWER- a path that travels along each edge of a graph once and only
once
,Math 110 - Chapter 5,6,7,8,9 Terms with
more than 115 correct answers.
Euler Circuit - ANSWER- a circuit that travels along each edge of a graph once and only
once
Connected Graph - ANSWER- a graph such that there is a path going from any vertex
to any other vertex
Disconnected Graph - ANSWER- a graph that is disconnected; it has two or more
connected components
Components - ANSWER- the connected "pieces" that make up a graph
Bridge - ANSWER- an edge in a connected graph without which the graph would be
disconnected
Random Variable - ANSWER- a variable whose value is a numerical outcome of a
probability experiment
discrete random variable - ANSWER- a random variable that can take one of a finite
number of distinct outcomes
examples of discrete random variables - ANSWER- 1. The number that comes up on a
roll of a dice.
2. The number of siblings a randomly chosen person has.
continuous random variables - ANSWER- random variables that can take on any value
in an interval
examples of continuous random variables - ANSWER- 1. The height of a randomly
chosen college student.
2. The amount of electricity used to light a randomly selected classroom.
probability distribution - ANSWER- specifies the probability for each possible value of
the random variable
Properties of a probability distribution - ANSWER- A. 0 ≤ P(x) ≤ 1 for every possible x-
value
[Every value of P(x) is between 0 and 1]
B. ΣP(x) = 1
[If you add up every P(x), you get 1]
Example: Decide if the following is a probability distribution:
, Math 110 - Chapter 5,6,7,8,9 Terms with
more than 115 correct answers.
x-values: 1, 2, 3, 4
P(x): 0.25, 0.65 -0.3, 0.11 - ANSWER- This is not a probability distribution. P(x=3) = -
0.3, which is not between 0 and 1.
Example: Four patients have made appointments to have their blood pressure checked
at a clinic. Let X be the number of them that have high blood pressure. The probability
distribution of X is:
(a) Find P(2 or 3)
(b) Find P(More than 1)
(c) Find P(At least 1) - ANSWER- First: Verify that it is a probability distribution
0.23 + 0.41 + 0.27 + 0.08 + 0.01 = 1
Notice that the events are mutually exclusive.
(a) P(2 or 3) = P(2) + P(3) by the addition rule.
= 0.27 + 0.08
= 0.35
mean of a random variable - ANSWER- Provides a measure of center for the probability
distribution of a random variable
NOTE: The mean is a measure of center of the probability distribution.
Calculating the Mean of a random variable - ANSWER- μx = Σ[x*P(x)]
The mean of a random variable = sum of all [x * P(x)]
Example: A computer monitor is composed of pixels. It is not uncommon for a few of
these to be defective. Let X represent the number of defective pixels on a randomly
chosen monitor. The probability distribution of X is as follows. Find the mean number of
defective pixels:
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