STA 032代写、代做R编程语言、代写R Markdown、R设计代做

日期：2019-05-26 11:22

STA 032 Spring 2019

R Report II - Due Friday, May 31st by 5:00pm.

R Report II

FORMAT

* Use set.seed(10) at the beginning of your document.

* Use complete sentences and proper grammar to answer all questions.

* Use R Markdown to create an html document. Write in a report style format.

* Code should not be in the body of the text, so be sure to add echo = FALSE in the preface to your R chunks. All code

should be included at the end of the homework, as an appendix.

I. Simulate a binomial random variable. Consider a class with 80 students, and the probability that a student does not

turn in a homework is 0.15 (a “success”). Assume all students are independent of all other students, and the probability

does not change.

(a) Use sample to simulate drawing 80 students who either do, or do not, turn in their homework, and then find the

total (out of 80) who did not turn in their homework. You should return one number, X = total # of students out

of 80 who did not turn in their homework.

(b) Repeat (a) 1000000 times (you should have 1000000 values for “number of successes”,or X), plot a histogram of your

result (do not print out the 1000000 values!!). For this particular binomial distribution, is the distribution

symmetric? Explain.

(c) Find the average of the number of successes in 80 trials and the standard deviation based on your simulation from

part (b).

(d) Estimate the probability that all students turned in their homework based on your simulation from (b).

(e) Estimate the probability that at least four students did not turn in their homework based on your simulation from

part (b).

(f) What is the median number of students who will forget their homework based on your simulation from (b)?

II. The goal of this problem is to simulate the distribution of the sample mean. We will use the built in dataset lynx. To

load the dataset and avoid some problems, copy and paste the following command:

lynx = as.numeric(lynx)

Assume this vector represents the population. I.e., the mean of this vector is our “true mean”.

(a) Draw a histogram of the population, find the “true” mean, and the “true” variance. Does this data look normally

distributed?

(b) Draw a random sample of size 10 from the population, and report back the mean of your sample.

(c) Repeat part (b) 1000000 times. You should have a vector of 1000000 means. Find the mean of that vector, and the

standard deviation of that vector. Plot a histogram.

(d) Draw a random sample of size 50 from the population, and report back the mean of your sample.

(e) Repeat part (d) 1000000 times. You should have a vector of 1000000 means. Did the mean and standard deviation

increase, decrease, or stay approximately the same from (c)?

(f) Plot a histogram of the vector in (e) and describe the shape. What did you notice as the sample size increased?

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