Please Do the part d,e,f,g and h of the question.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section10.8: Probability
Problem 19E
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Please Do the part d,e,f,g and h of the question.
thanks
![In this question, you will explore a new distribution called the uniform distri-
bution and use R to conduction a simulation that demonstrates how the CLT works.
A uniform random variable is a continuous random variable which PDF looks like a
rectangle. It has two parameters: 1) a which specifies the minimum value of the random
variable, and 2) b which specifics the maximum value of the random variable. We usually
denote a uniform random variable X as X~ Uniform(a, b). In R, the runif() function
can be used to generate data from the uniform distribution. In runif (), the default
values for parameters a and b are 0 and 1. Read the help page for runif () and perform
the following:
(a) Generate 1000 data points from Uniform(0, 1). Attach your code.
(b) Use hist() function to draw a histogram of the 1000 data points you generated in
part (a). Describe the shape of the histogram in words. Attach the code and the
histogram.
(c) Now we will use demonstrate how the CLT works. Generate 30 data points from
Uniform(0, 1). Attach the code.
(d) Draw a histogram of the 30 data points. Describe the shape of the histogram in
words. Attach the code and the histogram.
(e) Compute the sample mean of the 30 data points. What is the value of the sample
mean? Attach code.
(f) Use replicate () function to repeat parts (c) and (e) 1000 times. Now you should
have 1000 sample means. Attach your code.
(g) Draw a histogram of the 1000 sample means. Attach the code and the histogram.
(h) Does the histogram in part (g) look normal? Why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d77d84a-20ec-4377-a892-8a5769edf2b5%2F45790495-6228-4e40-8e99-735c15b30239%2Fu153219_processed.jpeg&w=3840&q=75)
Transcribed Image Text:In this question, you will explore a new distribution called the uniform distri-
bution and use R to conduction a simulation that demonstrates how the CLT works.
A uniform random variable is a continuous random variable which PDF looks like a
rectangle. It has two parameters: 1) a which specifies the minimum value of the random
variable, and 2) b which specifics the maximum value of the random variable. We usually
denote a uniform random variable X as X~ Uniform(a, b). In R, the runif() function
can be used to generate data from the uniform distribution. In runif (), the default
values for parameters a and b are 0 and 1. Read the help page for runif () and perform
the following:
(a) Generate 1000 data points from Uniform(0, 1). Attach your code.
(b) Use hist() function to draw a histogram of the 1000 data points you generated in
part (a). Describe the shape of the histogram in words. Attach the code and the
histogram.
(c) Now we will use demonstrate how the CLT works. Generate 30 data points from
Uniform(0, 1). Attach the code.
(d) Draw a histogram of the 30 data points. Describe the shape of the histogram in
words. Attach the code and the histogram.
(e) Compute the sample mean of the 30 data points. What is the value of the sample
mean? Attach code.
(f) Use replicate () function to repeat parts (c) and (e) 1000 times. Now you should
have 1000 sample means. Attach your code.
(g) Draw a histogram of the 1000 sample means. Attach the code and the histogram.
(h) Does the histogram in part (g) look normal? Why?
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