class: center, middle, inverse, title-slide

.title[
# Simulation of Normal Distribution
]
.subtitle[
## National Taipei University
]
.author[
### Andy Yeh
]
.date[
### 2022-06-22
]

---

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  float: left;
  width: 50%;
 }
 .right-column {
  float: right;
  width: 50%;
 }
 .pull-right ~ p {
  clear: both;
 }
 </style>

## Introduction

Normal distribution shows everywhere in our life. For observing what the values my emerge in our real world, I simulation 100 samples from **N(0, 1)** and get 100 pairs from **bivariate normal distribution with the mean vector (0, 0) as well as covariance identity matrix**. Then, visualize these data points by ggplot packages. Here is my code.

[Normal samples](#Normal_samples)

[Normal graph](#Normal_graph)

[Bivariate samples](#Bivariate_samples)

[Bivariate graph](#Bivariate_graph)

---
name: Normal_samples

## Normal Samples

- show 5 of 100 samples

```r
print(normalSamples[1:5])
```

```
## [1]  0.33631074 -0.03944977  0.62006680 -2.02877404 -0.91322833
```

---

name: Normal_graph

## Normal Graph
.left-column[
Although normal distribution is symmetric, it doesn't mean our sample must be falls apart from x =0 equal. As we see in this graph, this distribution is slightly skew.
]
.right-column[
![](OneDimensionNormal.png)
]

---

name: Bivariate_samples

## Bivariate Samples

- show 5 of 100 samples

```r
print(bivariateSample[1:5,])
```

```
##            [,1]       [,2]
## [1,]  0.1813740 -0.7435546
## [2,] -0.9353029  0.1407214
## [3,]  0.9438925 -0.3515571
## [4,] -1.3254220  0.9775177
## [5,]  0.4904515 -0.2487180
```

---

name: Bivariate_graph

## Bivariate Graph

.left-column[
This setting of bivariate normal distribution makes the 1000 points easily center at the coordinate (0, 0) and the dispersion of y axis 0 is similar to that of x axis. In this graph, the sample has verify this think.
]
.right-column[

![](TwoDimensionNormal.png)

]

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Simulation of Normal Distribution
National Taipei University
Andy Yeh
2022-06-22
1

Introduction

Normal distribution shows everywhere in our life. For observing what the values my emerge in our real world, I simulation 100 samples from N(0, 1) and get 100 pairs from bivariate normal distribution with the mean vector (0, 0) as well as covariance identity matrix. Then, visualize these data points by ggplot packages. Here is my code.

Bivariate samples

Bivariate graph

2

Normal Samples

show 5 of 100 samples

print(normalSamples[1:5])

## [1]  0.33631074 -0.03944977  0.62006680 -2.02877404 -0.91322833

3

Normal Graph

Although normal distribution is symmetric, it doesn't mean our sample must be falls apart from x =0 equal. As we see in this graph, this distribution is slightly skew.

4

Bivariate Samples

show 5 of 100 samples

print(bivariateSample[1:5,])

##            [,1]       [,2]
## [1,]  0.1813740 -0.7435546
## [2,] -0.9353029  0.1407214
## [3,]  0.9438925 -0.3515571
## [4,] -1.3254220  0.9775177
## [5,]  0.4904515 -0.2487180

5

Bivariate Graph

This setting of bivariate normal distribution makes the 1000 points easily center at the coordinate (0, 0) and the dispersion of y axis 0 is similar to that of x axis. In this graph, the sample has verify this think.

6

Introduction

Normal distribution shows everywhere in our life. For observing what the values my emerge in our real world, I simulation 100 samples from N(0, 1) and get 100 pairs from bivariate normal distribution with the mean vector (0, 0) as well as covariance identity matrix. Then, visualize these data points by ggplot packages. Here is my code.

Bivariate samples

Bivariate graph

2

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