4 Homework Problem H4: This problem combined with Homework Problem H5 makes some key comparisons between Chapters 6 and 7. a) Verify that the function f(x) = with the domain (2,5,10} is a valid p.d.f %3D -+x- 20 20 of a discrete random variable X. 3-x b) It can be verified that the function f(x)=,C, with the domain of {0,1,2,3} is a valid random variable X. Note: this function is an example of a binomial probability distribution function. c) Without using any statistical features of your graphing calculator, using the function from part b) above, compute P(X = 2). d) Without using any statistical features of your graphing calculator, using the function in part b) above, compute P(X 2 2). e) General Rule for finding probability in all cases when X is discrete (as opposed to being continuous): If f is a probability distribution function (p.d.f.) of a discrete random variable X defined on the domain {x,,x2, x3,.., X }, then P(x, s X < x) (where / and m are two integers such that 1<1 ). %3D Homework Problem H7: If X N(10,3) and the area under its normal curve between x, = 5.5 and x, = 16 is approximately 85.56%, then the area under the standard normal curve between z, = -1.5 and z, = 2 is of your graphing calculator nor tables for this problem) because 5.5 is deviations of 3 above 10 and -1.5 is also because 16 is deviations of 1 above 0. %3D (do not use any statistical commands %3D standard standard deviations of 1 above 0, and standard deviations of 3 above 10 and 2 is also standard Homework Problem H8: Consider the function f seen in part b) of the Homework Problem H5. a) Draw its graph. b) Verify that this function f is a valid probability density function of a continuous random variable X. c) Compute P(X 1). d) Compute P(X >1). e) Compute P(X > 1).
4 Homework Problem H4: This problem combined with Homework Problem H5 makes some key comparisons between Chapters 6 and 7. a) Verify that the function f(x) = with the domain (2,5,10} is a valid p.d.f %3D -+x- 20 20 of a discrete random variable X. 3-x b) It can be verified that the function f(x)=,C, with the domain of {0,1,2,3} is a valid random variable X. Note: this function is an example of a binomial probability distribution function. c) Without using any statistical features of your graphing calculator, using the function from part b) above, compute P(X = 2). d) Without using any statistical features of your graphing calculator, using the function in part b) above, compute P(X 2 2). e) General Rule for finding probability in all cases when X is discrete (as opposed to being continuous): If f is a probability distribution function (p.d.f.) of a discrete random variable X defined on the domain {x,,x2, x3,.., X }, then P(x, s X < x) (where / and m are two integers such that 1<1 ). %3D Homework Problem H7: If X N(10,3) and the area under its normal curve between x, = 5.5 and x, = 16 is approximately 85.56%, then the area under the standard normal curve between z, = -1.5 and z, = 2 is of your graphing calculator nor tables for this problem) because 5.5 is deviations of 3 above 10 and -1.5 is also because 16 is deviations of 1 above 0. %3D (do not use any statistical commands %3D standard standard deviations of 1 above 0, and standard deviations of 3 above 10 and 2 is also standard Homework Problem H8: Consider the function f seen in part b) of the Homework Problem H5. a) Draw its graph. b) Verify that this function f is a valid probability density function of a continuous random variable X. c) Compute P(X 1). d) Compute P(X >1). e) Compute P(X > 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
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![4
Homework Problem H4: This problem combined with Homework Problem H5 makes
some key comparisons between Chapters 6 and 7.
a) Verify that the function f(x) =
with the domain (2,5,10} is a valid p.d.f
%3D
-+x-
20
20
of a discrete random variable X.
3-x
b) It can be verified that the function f(x)=,C,
with the domain
of
{0,1,2,3} is a valid
random variable X. Note: this function is an example of a
binomial probability distribution function.
c) Without using any statistical features of your graphing calculator, using the
function from part b) above, compute P(X = 2).
d) Without using any statistical features of your graphing calculator, using the
function in part b) above, compute P(X 2 2).
e) General Rule for finding probability in all cases when X is discrete (as opposed to
being continuous):
If f is a probability distribution function (p.d.f.) of a discrete random variable X
defined on the domain {x,,x2, x3,.., X }, then P(x, s X < x) (where / and m
are two integers such that 1<1<msk) is found by
corresponding probability values, so
P(x, sX S x)= P(X = x,)+ P(X =x, +...+P(X = x); that is,
P(x, < X < x,)= f(x,)+ f(x) +.. + f(x,).
all the
Homework Problem H5: This problem combined with Homework Problem H4 makes
some key comparisons between Chapters 6 and 7.
1
a) Verify that the function f(x) =- with its domain being the interval [5,10] is a
%3D
valid p.d.f. of a continuous random variable X. Note: this is the function you
graphed in homework exercise 18 in section 7.1.
b) Consider the function f(x)= -
with the domain being the interval
5/2n
(-0, 00) (you do not need to memorize this formula). This function is called the
normal probability density function with mean 11 and standard deviation 5. It can
be verified that this function is a valid
of a
random variable X.
c) Using the function from part a) above, compute P(X = 7).
d) Using the function from part a) above, compute P(X 2 7).
e) General Rule for finding P(a s X <b) in all cases when X is continuous (as
opposed to being discrete): If f is a probability density function (p.d.f.) of a
continuous random variable X, then P(a s X <b) is found by computing the
%3D
under the
of f from
to
3.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80f8f25a-c3b4-4d15-945c-0673001929d8%2F5a665622-0580-4f13-9557-330c211d48c3%2Frgbfoip.jpeg&w=3840&q=75)
Transcribed Image Text:4
Homework Problem H4: This problem combined with Homework Problem H5 makes
some key comparisons between Chapters 6 and 7.
a) Verify that the function f(x) =
with the domain (2,5,10} is a valid p.d.f
%3D
-+x-
20
20
of a discrete random variable X.
3-x
b) It can be verified that the function f(x)=,C,
with the domain
of
{0,1,2,3} is a valid
random variable X. Note: this function is an example of a
binomial probability distribution function.
c) Without using any statistical features of your graphing calculator, using the
function from part b) above, compute P(X = 2).
d) Without using any statistical features of your graphing calculator, using the
function in part b) above, compute P(X 2 2).
e) General Rule for finding probability in all cases when X is discrete (as opposed to
being continuous):
If f is a probability distribution function (p.d.f.) of a discrete random variable X
defined on the domain {x,,x2, x3,.., X }, then P(x, s X < x) (where / and m
are two integers such that 1<1<msk) is found by
corresponding probability values, so
P(x, sX S x)= P(X = x,)+ P(X =x, +...+P(X = x); that is,
P(x, < X < x,)= f(x,)+ f(x) +.. + f(x,).
all the
Homework Problem H5: This problem combined with Homework Problem H4 makes
some key comparisons between Chapters 6 and 7.
1
a) Verify that the function f(x) =- with its domain being the interval [5,10] is a
%3D
valid p.d.f. of a continuous random variable X. Note: this is the function you
graphed in homework exercise 18 in section 7.1.
b) Consider the function f(x)= -
with the domain being the interval
5/2n
(-0, 00) (you do not need to memorize this formula). This function is called the
normal probability density function with mean 11 and standard deviation 5. It can
be verified that this function is a valid
of a
random variable X.
c) Using the function from part a) above, compute P(X = 7).
d) Using the function from part a) above, compute P(X 2 7).
e) General Rule for finding P(a s X <b) in all cases when X is continuous (as
opposed to being discrete): If f is a probability density function (p.d.f.) of a
continuous random variable X, then P(a s X <b) is found by computing the
%3D
under the
of f from
to
3.
![f) Read both questions and answers to parts a) in problems H4 and H5.
How they are similar and how they are different? Do the same for art
b), parts c), parts d) and parts e) from those problems.
Homework Problem H6:
In this problem consider the function f(x)=-x+
1
with its domain being defined
%3D
8.
here as the interval [0,4].
a) Draw the graph of f.
b) Verify that the functionf is a valid probability density function of a continuous
random variable X.
c) Compute P(X 1).
d) Compute P(X 21).
e) Compute P(X > ).
%3D
Homework Problem H7:
If X N(10,3) and the area under its normal curve between x, = 5.5 and x, = 16 is
approximately 85.56%, then the area under the standard normal curve between
z, = -1.5 and z, = 2 is
of your graphing calculator nor tables for this problem) because 5.5 is
deviations of 3 above 10 and -1.5 is also
because 16 is
deviations of 1 above 0.
%3D
(do not use any statistical commands
%3D
standard
standard deviations of 1 above 0, and
standard deviations of 3 above 10 and 2 is also
standard
Homework Problem H8:
Consider the function f seen in part b) of the Homework Problem H5.
a) Draw its graph.
b) Verify that this function f is a valid probability density function of a continuous
random variable X.
c) Compute P(X 1).
d) Compute P(X >1).
e) Compute P(X > 1).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F80f8f25a-c3b4-4d15-945c-0673001929d8%2F5a665622-0580-4f13-9557-330c211d48c3%2F3xfd8z5.jpeg&w=3840&q=75)
Transcribed Image Text:f) Read both questions and answers to parts a) in problems H4 and H5.
How they are similar and how they are different? Do the same for art
b), parts c), parts d) and parts e) from those problems.
Homework Problem H6:
In this problem consider the function f(x)=-x+
1
with its domain being defined
%3D
8.
here as the interval [0,4].
a) Draw the graph of f.
b) Verify that the functionf is a valid probability density function of a continuous
random variable X.
c) Compute P(X 1).
d) Compute P(X 21).
e) Compute P(X > ).
%3D
Homework Problem H7:
If X N(10,3) and the area under its normal curve between x, = 5.5 and x, = 16 is
approximately 85.56%, then the area under the standard normal curve between
z, = -1.5 and z, = 2 is
of your graphing calculator nor tables for this problem) because 5.5 is
deviations of 3 above 10 and -1.5 is also
because 16 is
deviations of 1 above 0.
%3D
(do not use any statistical commands
%3D
standard
standard deviations of 1 above 0, and
standard deviations of 3 above 10 and 2 is also
standard
Homework Problem H8:
Consider the function f seen in part b) of the Homework Problem H5.
a) Draw its graph.
b) Verify that this function f is a valid probability density function of a continuous
random variable X.
c) Compute P(X 1).
d) Compute P(X >1).
e) Compute P(X > 1).
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