title: “Week 2 Lab, MAST20005/MAST90058”
author: “School of Mathematics and Statistics, University of Melbourne”
date: “Semester 2, 2022”
institute: “University of Melbourne”
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**Goals:** (i) Getting started with R and RStudio; (ii) Basic exploratory data
analyses; (iii) Basic graphics.
# R introduction and reference
This guide is available online at:
This online guide is much longer than the usual weekly lab notes. You are not
expected to absorb it completely in a single lab session.We suggest you skim
it upon first reading and ensure you set aside **at least 15 minutes** to work
through the lab exercises at the end of your first lab class, referring back to
the online guide when required.
# Exercises
1. Calculate $sum_{i=1}^{100} ln(i)$.
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2. Let $X sim mathrm{N}(1, 2)$.What is $mathbb{E}(X^2)$?Approximate this
by simulating a large number of normal random variables and doing an appropriate calculation.
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3. Use the help system to find out what the `qnorm()` function does. Explain
the result of running `qnorm(0.1)`.What about `qnorm(0.1, lower.tail
= FALSE)`?For what value of `a` will the command `qnorm(a)` return the same
value as the previous one?
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4. Write a function `exp1pdf()` that calculates the pdf of an exponential
distribution with mean 1.Compare the output of your function against the
in-built function that does the same calculation (`dexp()`).Remember to check
it works for all inputs: for example, what is the correct value of
`exp1pdf(-1)`?
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5. Do question 6(c) from the tutorial problems.
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6. Do question 7(b) from the tutorial problems.
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7. Do question 2(c) from the tutorial problems by simulation (rather than using
the Central Limit Theorem).
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