Statistical Analysis

0 covered of 17 dot points

Lessons

Nothing written for this module yet. The dot points are listed beside this, so you can still see exactly what the module asks of you and take it to the official syllabus.

What the syllabus asks

ME-S1 The Binomial Distribution

use a Bernoulli random variable as a model for two-outcome situations (ACMMM143)ACMMM143
not written yet · needs a worked example
- identify contexts suitable for modelling by Bernoulli random variables (ACMMM144)ACMMM144
  not written yet · needs a worked example
use Bernoulli random variables and their associated probabilities to solve practical problems (ACMMM146) AAMACMMM146
not written yet · needs a worked example
- understand and apply the formulae for the mean, $E (X) = \overline{x} = p$ , and variance, $Var (X) = p (1 - p)$ , of the Bernoulli distribution with parameter $p$ , and $X$ defined as the number of successes (ACMMM145)ACMMM145
  not written yet · needs a worked example
understand the concepts of Bernoulli trials and the concept of a binomial random variable as the number of ‘successes’ in $n$ independent Bernoulli trials, with the same probability of success $p$ in each trial (ACMMM147)ACMMM147
not written yet
- calculate the expected frequencies of the various possible outcomes from a series of Bernoulli trials
  not written yet · needs a worked example
use binomial distributions and their associated probabilities to solve practical problems (ACMMM150) AAMACMMM150
not written yet · needs a worked example
- identify contexts suitable for modelling by binomial random variables (ACMMM148)ACMMM148
  not written yet · needs a worked example
- identify the binomial parameter $p$ as the probability of success
  not written yet
- understand and use the notation $X Bin (n, p)$ to indicate that the random variable $X$ is distributed binomially with parameters $n$ and $p$
  not written yet
- apply the formulae for probabilities $P (X = r) =^{n} C_{r} p^{r} (1 - p)^{n - r}$ associated with the binomial distribution with parameters $n$ and $p$ and understand the meaning of $^{n} C_{r}$ as the number of ways in which an outcome with $r$ successes can occur
  not written yet · needs a worked example
- understand and apply the formulae for the mean, $E (X) = \overline{x} = n p$ , and the variance, $Var (X) = n p (1 - p)$ , of a binomial distribution with parameters $n$ and $p$
  not written yet · needs a worked example
use appropriate graphs to explore the behaviour of the sample proportion on collected or supplied data AAM
not written yet · needs a worked example
- understand the concept of the sample proportion $\overset{p}{^}$ as a random variable whose value varies between samples (ACMMM174)ACMMM174
  not written yet
explore the behaviour of the sample proportion using simulated data AAM
not written yet
- examine the approximate normality of the distribution of $\overset{p}{^}$ for large samples (ACMMM175)ACMMM175
  not written yet
understand and use the normal approximation to the distribution of the sample proportion and its limitations AAM
not written yet

Wording is the official syllabus, read from the NESA document by a parser. The full document.