For each of these random variables x, we could set up a table listing all the sample points in (2.4) and, next to each sample point, the corresponding value of æ. This table may remind you of the tables of values we could use in plotting the graph of a function. In analytical geometry or in a physics problem, knowing x as a function of t means that for any given t we can find the corresponding value of r. In probability the sample point corresponds to the independent variable t; given the sample point, we can find the corresponding value of the random variable r if we are given a description of r (for example, r = the sum of numbers on dice). The "description" corresponds to the formula x(t) that we use in plotting a graph in analytic geometry. Thus we may say that a random variable r is a function defined on a sample space. Probability Functions Let us consider further the random variable x = of numbers on dice" for a toss of two dice [sample space (2.4)]. We note that there are several sample points for which r = 5, namely the points marked a in (2.4). Similarly, there are several sample points for most of the other values of r. It is then "sum convenient to lump together all the sample points corresponding to a given value of x, and consider a new sample space in which each point corresponds to one value of x; this is the sample space (2.5). The probability associated with each point of the new sample space is obtained as in Section 2, by adding the probabilities associated with all the points in the original sample space corresponding to the particular value of r. Each value of r, say ri, has a probability p; of occurrence; we may write p; = f(x:) = probability that r = ri, and call the function f(x) the probability function for the random variable r. In (2.5) we have listed on the first line the values of x and on the second line the values of f(x). [In this problem, r and f(r) take on only a finite number of discrete values; in some later problems they will take on a continuous set of values.] We could also exhibit these values graphically (Figure 5.1). %3D p= f(x) 36 1 2 5 6. 7 8 10 11 12 Figure 5.1
For each of these random variables x, we could set up a table listing all the sample points in (2.4) and, next to each sample point, the corresponding value of æ. This table may remind you of the tables of values we could use in plotting the graph of a function. In analytical geometry or in a physics problem, knowing x as a function of t means that for any given t we can find the corresponding value of r. In probability the sample point corresponds to the independent variable t; given the sample point, we can find the corresponding value of the random variable r if we are given a description of r (for example, r = the sum of numbers on dice). The "description" corresponds to the formula x(t) that we use in plotting a graph in analytic geometry. Thus we may say that a random variable r is a function defined on a sample space. Probability Functions Let us consider further the random variable x = of numbers on dice" for a toss of two dice [sample space (2.4)]. We note that there are several sample points for which r = 5, namely the points marked a in (2.4). Similarly, there are several sample points for most of the other values of r. It is then "sum convenient to lump together all the sample points corresponding to a given value of x, and consider a new sample space in which each point corresponds to one value of x; this is the sample space (2.5). The probability associated with each point of the new sample space is obtained as in Section 2, by adding the probabilities associated with all the points in the original sample space corresponding to the particular value of r. Each value of r, say ri, has a probability p; of occurrence; we may write p; = f(x:) = probability that r = ri, and call the function f(x) the probability function for the random variable r. In (2.5) we have listed on the first line the values of x and on the second line the values of f(x). [In this problem, r and f(r) take on only a finite number of discrete values; in some later problems they will take on a continuous set of values.] We could also exhibit these values graphically (Figure 5.1). %3D p= f(x) 36 1 2 5 6. 7 8 10 11 12 Figure 5.1
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
![For each of these random variables x, we could set up a table listing all the sample
points in (2.4) and, next to each sample point, the corresponding value of æ. This
table may remind you of the tables of values we could use in plotting the graph
of a function. In analytical geometry or in a physics problem, knowing x as a
function of t means that for any given t we can find the corresponding value of r.
In probability the sample point corresponds to the independent variable t; given
the sample point, we can find the corresponding value of the random variable r if
we are given a description of r (for example, r = the sum of numbers on dice). The
"description" corresponds to the formula x(t) that we use in plotting a graph in
analytic geometry. Thus we may say that a random variable r is a function defined
on a sample space.
Probability Functions Let us consider further the random variable x =
of numbers on dice" for a toss of two dice [sample space (2.4)]. We note that there
are several sample points for which r = 5, namely the points marked a in (2.4).
Similarly, there are several sample points for most of the other values of r. It is then
"sum
convenient to lump together all the sample points corresponding to a given value
of x, and consider a new sample space in which each point corresponds to one value
of x; this is the sample space (2.5). The probability associated with each point
of the new sample space is obtained as in Section 2, by adding the probabilities
associated with all the points in the original sample space corresponding to the
particular value of r. Each value of r, say ri, has a probability p; of occurrence;
we may write p; = f(x:) = probability that r = ri, and call the function f(x) the
probability function for the random variable r. In (2.5) we have listed on the first
line the values of x and on the second line the values of f(x). [In this problem, r
and f(r) take on only a finite number of discrete values; in some later problems
they will take on a continuous set of values.] We could also exhibit these values
graphically (Figure 5.1).
%3D
p= f(x)
36
1
2
5
6.
7
8
10
11
12
Figure 5.1](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e90891c-639d-4ecf-ab46-560af815eb6a%2F7dc833c7-4c0b-4a99-b2db-5040b1919082%2Fs8kt0db.png&w=3840&q=75)
Transcribed Image Text:For each of these random variables x, we could set up a table listing all the sample
points in (2.4) and, next to each sample point, the corresponding value of æ. This
table may remind you of the tables of values we could use in plotting the graph
of a function. In analytical geometry or in a physics problem, knowing x as a
function of t means that for any given t we can find the corresponding value of r.
In probability the sample point corresponds to the independent variable t; given
the sample point, we can find the corresponding value of the random variable r if
we are given a description of r (for example, r = the sum of numbers on dice). The
"description" corresponds to the formula x(t) that we use in plotting a graph in
analytic geometry. Thus we may say that a random variable r is a function defined
on a sample space.
Probability Functions Let us consider further the random variable x =
of numbers on dice" for a toss of two dice [sample space (2.4)]. We note that there
are several sample points for which r = 5, namely the points marked a in (2.4).
Similarly, there are several sample points for most of the other values of r. It is then
"sum
convenient to lump together all the sample points corresponding to a given value
of x, and consider a new sample space in which each point corresponds to one value
of x; this is the sample space (2.5). The probability associated with each point
of the new sample space is obtained as in Section 2, by adding the probabilities
associated with all the points in the original sample space corresponding to the
particular value of r. Each value of r, say ri, has a probability p; of occurrence;
we may write p; = f(x:) = probability that r = ri, and call the function f(x) the
probability function for the random variable r. In (2.5) we have listed on the first
line the values of x and on the second line the values of f(x). [In this problem, r
and f(r) take on only a finite number of discrete values; in some later problems
they will take on a continuous set of values.] We could also exhibit these values
graphically (Figure 5.1).
%3D
p= f(x)
36
1
2
5
6.
7
8
10
11
12
Figure 5.1
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