stats_ch5_notes dStem

stats_chapter5.pdf

Overview:

• Density plot
• Density functions
• Probility

Contionous random variable Y: 3 properties:

• |Y| = $\infty$
• cont
• $P(Y)=x?0$ (prob of y = certain value =0)

Defition of variaence of Y? (p.24)

$$\begin{array}{c}{\sigma }^2=v(y)=E((y-\mu {)}^2)\end{array}$$

Density Function

Knowing Y, and cumlative distribution func as F(y) then can define it as the derative of Y, formally:

$$\begin{array}{c}F(y_0)=P(Y\le y_0),-\infty <y_0<\infty \\ \text{then: }f(y)=\frac{dF(y)}{dy}\\ f(y)\ge 0\\ F(\infty )=0\\ P(a<Y<b)=F(b)-F(a)\end{array}$$

Plotting Density func (review later mayb -rm)

curve(
dbinom(x,
      mean=10
      sd=5
      ),
      xlim=c(10-3n*5,10+3m*5)
)

$$\begin{array}{c}P(2\le x\le 12)\dots \end{array}$$

Takeaaways:

$$\begin{array}{c}Y=aX+b\\ V(Y)=a^2(V(x))\end{array}$$

Using integrate function does not (show your work) sohuld be done by hand

Example Problem (slide 15)

Uniform distributions (dpqr-norm)

• dnorm: Height of normal
• lower tail area of the Normal up to given y

Central Limit Therom

New keywords

polygon #
 

Ways to determine normality:

• Histogram/stem&leaf
• .
• qqplot

Gamma probailitiy distro

• $\gamma$ = density, gamma density
• $\Gamma$ = gamma function = makes AUC ($\int$) = 1

Weibull

• Dont need to know proof, just how code works..

Stuff you need to do:

• Given distro + params → find prob?
• Find dpqr!
• plot density
• calculate probility {wait isnt this dpqr? Check..} (it must use a p function!)

Exam

• Ch 1-6
• Work out z
• boxplot for outliers general plots
• wrangle
  • Have the [] and dylyr
• tables
  • and/or/given/marginal
• outliers
• Random variables dpqr eg. $P(x,y,z$ )
  • Will have paragraph problem,
• barplots out of table know options + how 2 play around w/ it..
• YOU MAY NOT USE PACKAGE IN EXAM
• exam designed to be busy, will be time constraint! !time looking for things
• Review: Assignment/slides/quizzes