STA258 Lecture 03

Pre-Lecture

2. Descriptive Statistics.pdf
STA258 Pre-Lecture 03 Summary

Lecture

• Normal Distribution
• Gaussian Function
• The above shows how we get from the Gaussian Function to a Normal Distribution and Standard Normal Distribution.
• $X\sim \mathrm{\Gamma }(\alpha ,\beta )$
  • $\mathrm{E}[X]=\alpha \beta$
  • $\mathrm{Var}(X)=\alpha {\beta }^2$
• Standard Normal Distribution
• Ex:
  • Time taken for an employee in a company to do a task is Normal Distribution with $\mu =60$ and $\sigma =5$
  • What is the probability that it takes more than $68$ minutes
  • $P(X\ge 68)$
  • $P(\frac{X-\mu }{\sigma }\ge \frac{68-\mu }{\sigma })$
  • $P(\frac{X-60}{5}\ge \frac{8}{5})$
  • $P(Z\ge \frac{8}{5})$
  • $P(Z\ge 1.6)=1-0.9452=0.0548$
  • What is the probability this employee takes between $50\to 65$
  • $P(50\le X\le 65)$
  • $P(-2\le Z\le 1)=\mathrm{\Phi }(1)-\mathrm{\Phi }(-2)=1-(0.0228+0.1587)=0.8185$
• Normal Q-Q Plot
• Messing with R
  • 
  • Ex:
    • Covid 19, day 1, patient 0 is an outlier.
    • If you ignore it, then you have an outbreak, if you look at it, then you'll see what it is.
    • Analyse the outliers properly.
  • 
  • You can see that it might not be an outlier, when we separate by species, different species have different data. We only have on outlier in this case instead of ~5.