Week1

Lecture Notes

https://class.coursera.org/statinference-008/wiki/Lecture_Notes http://bcaffo.github.io/courses/06_StatisticalInference/homework/hw1.html#1

Beta Function

See http://www.xycoon.com/beta.htm

# Triangle Shape  where 75 percentile is
pbeta(0.75, 2, 1)

## [1] 0.5625

# Flat Horiz Line where 75 percentile is
pbeta(0.75, 1, 1)

## [1] 0.75

A random variable

takes the value -4 with probability .2 and 1 with probability .8. What is the variance of this random variable?

(-4)^2*0.2 + (1^2)*0.8

## [1] 4

Probability Mass Function - What’s the Variace?

p <- c(.1, .2, .3, .4)
x <- 2:5 
sum(x^2*p)-sum(x*p)^2

## [1] 1

Sum of PMF (Probability Mass Function)

x <- 1:4
p <- x/sum(x)
temp <- rbind(x, p)
rownames(temp) <- c("X", "Prob")
temp

##      [,1] [,2] [,3] [,4]
## X     1.0  2.0  3.0  4.0
## Prob  0.1  0.2  0.3  0.4

sum(p*x)

## [1] 3

1.0*0.1 + 2.0*0.2 + 3.0*0.3 + 4.0*0.4

## [1] 3