Central Limit Theorem

Load Packages

library(knitr)
library(matlib)

Problem 1

The answers are in the following pages. The calculations of (a), (b), (c) are shown in the code chunks.

v <- 365 * (1/4)
x <- pnorm(100 - 100, mean = 0, sd = sqrt(v), lower.tail = FALSE)
x

## [1] 0.5

The Expected Value of Y365 being 100, Probability of Y365 >= 100, is just the area under second half of the Normal Curve.

x <- pnorm(110 - 100, mean = 0, sd = sqrt(v), lower.tail = FALSE)
x

## [1] 0.1475849

The further one goes from the mean (Expected Value), the area on the positive reduces.

x <- pnorm(120 - 100, mean = 0, sd = sqrt(v), lower.tail = FALSE)
x

## [1] 0.01814355

Reduces even further.

Problem 2

Problem 3

Marker: 605-09