[SOLVED] MAST20005/MAST90058

title: Week 2 Lab, MAST20005/MAST90058
author: School of Mathematics and Statistics, University of Melbourne
date: Semester 2, 2022
institute: University of Melbourne

Copyright By Assignmentchef assignmentchef

fontsize: 11pt
classoption: a4paper
html_document:
toc_float:
collapsed: false

**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 $sum_{i=1}^{100} ln(i)$.
# Insert answer here

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.
# Insert answer here

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?
# Insert answer here

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)`?
# Insert answer here

5. Do question 6(c) from the tutorial problems.
# Insert answer here

6. Do question 7(b) from the tutorial problems.
# Insert answer here

7. Do question 2(c) from the tutorial problems by simulation (rather than using
the Central Limit Theorem).
# Insert answer here

CS: assignmentchef QQ: 1823890830 Email: [email protected]