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create_matrix_triangular_simulate_Normal_Restricted.rmd
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create_matrix_triangular_simulate_Normal_Restricted.rmd
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---
title: "create_matrix_triangular_simulate_Normal_Restricted"
output: github_document
---
```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
Sys.setenv(RSTUDIO_PANDOC = "C:/Program Files/RStudio/bin/quarto/bin/tools")
```
## Ex I.
#### A function that takes a square matrix and sets it to zero above the main diagonal
```{r}
fun_tri_mat <- function(A){
D <- dim(A)
if(D[1] != D[2]) stop("A must be square matrix")
n <- D[1]
for(i in 1:(n-1)){
for(j in (i+1):n){
A[i, j] <- 0
}
}
return(A)
}
A <- matrix(1, 4, 4)
A
A2 <- fun_tri_mat(A)
A2
```
***
## EX II.
#### A function that is a normal sample of the given limits, in such a way that the simulated
#### values must be larger than the specified value of A and smaller than the specified value of B.
#### In this function, the size of the production sample and the user's desired mean and standard deviation,
#### as well as the user's desired limits, are given in the function arguments.
```{r}
create_normal_restrict <- function(size,
Mu, Sig, a, b){
i = 0
Sample <- c()
while(i <= size){
temp1 <- rnorm(1, Mu, Sig)
if(temp1 < b && temp1 > a){
i = i + 1; Sample[i] <- temp1
}
}
return(Sample)
}
s <- create_normal_restrict(size = 10, Mu = 0, Sig = 2, a = 2, b = 4)
s
all(s > 2) && all(s < 4)
```
***
## EX III.
#### Edit code for EX II.
```{r}
create_normal_restrict <- function(size,
Mu, Sig, a, b){
Sample <- c()
for(i in 1:size){
temp1 <- rnorm(1, Mu, Sig)
while(temp1 < a || temp1 > b){
temp1 <- rnorm(1, Mu, Sig)
}
Sample[i] <- temp1
}
return(Sample)
}
s <- create_normal_restrict(size = 20, Mu = 2, Sig = 3, a = 3, b = 5)
s
all(s > 3) && all(s < 5)
```
***
## EX IV.
#### Simulation to prove the weak law of large numbers
```{r}
Weak_law_large_num <- function(size, Mu, showPlot = TRUE){
n <- size
E <- list()
for(i in 1:n){
E[[i]] <- rnorm(i, mean = Mu, sd = 1)
}
E_mean <- unlist(lapply(E, mean))
list_result <- list(Mean_result = E_mean, list_result = E)
if(showPlot){
plot(x = 1:n, y = E_mean, col = "darkblue", type = "l", xlab = "size of sample", ylab = "Sample Mean")
abline(h = Mu, lwd = 1.5, lty = 2, col = "yellow")
legend("topright", legend = expression(mu), lty = 2, lwd = 3, col = "yellow", bg = "black", cex = 3,
text.col = "white")
}
return(list_result)
}
Result <- Weak_law_large_num(size = 1e+4, Mu = 2.5, showPlot = T)
E <- Result$list_result
E[[5]]
E[[10]]
E[[20]]
E[[50]]
```