Your lab and homework submissions should be **well-formatted**, **well-written**, and **include comments** as-appropriate.

**Markdown:** You should use Markdown to help organize your work. The markup characters `#`, `##`, `###`, etc., will generate headers, sub-headers, sub-sub-headers, etc., in the resulting HTMl file. You should use these to generate headers for your labs and homeworks, such as

# Part I

## Problem 1

for the first problem in the first part of your lab.

# Part II

## Problem 4

### Part a

**Code Chunks:** All code that functions as a unit (for example, provides a solution to a single sub-problem in the lab) should be in its own code chunk:

```{r}
# All of the code to do Problem 4(a) should be here.

```

**Comments:** If you are doing something non-obvious in your code, you should include in-line comments explaining the purpose of parts of the code. What counts as "non-obvious" will depend on the programming and statistical background of the reader and will thus vary from person-to-person. For now, include comments liberally.

*Example:* Don't worry if you don't completely understand what this code chunk is doing. Hopefully, if I have commented it well, you should be able to infer what each part is doing using what you learned in introductory statistics!

```{r}
# The following code computes a 1 - alpha confidence interval
# for a population mean under a Gaussian population model with
# the population standard deviation known:

n     <- 5  # The sample size
xbar  <- 5  # The sample mean
sigma <- 10 # The population standard deviation

c <- 0.95 # The confidence level
alpha <- 1 - c # The area in both tails

# The critical value that puts area alpha / 2 in the right
# tail of a standard Gaussian density:

z.crit <- qnorm(1 - alpha/2)

# The margin of error for the sample mean

E <- sigma/sqrt(n)

# A confidence level c = 1 - alpha confidence interval
# for the population mean:

C <- xbar + c(-1, 1)*E
C

```

# Part III

## Problem 6

### Part b

**Explanations:** If a problem asks a question that requires a written response, you should write your response **in complete sentences** as plain text.

**Math Expressions:** Ideally (though I will not grade you on this), you should use LaTeX to typeset mathematical expressions. For example, typing \(\lambda\) will typeset the lowercase Greek letter lambda, \(\sigma^{2}\) will typeset the lowercase Greek letter sigma raised to the second power, etc. See Section 16.11 of **R Cookbook** for more on LaTeX, or ask me if you want to know how to typeset a given mathematical expression.