lab3.Rmd

---
title: "Lab 3!"
author: "winnie ngare"
date: "September 28, 2017"
output: html_notebook
---



###Q1
####Random selection of cars as **training dataset(40) and **test dataset(53) from the MASS Package.

```{r}
library(MASS)
df <- Cars93
nrow(df)

index.full <- 1:93
set.seed(20)
{training.data <- sample(1:93,40,replace = FALSE)
test.data <- df[-training.data,]
train.data <- df[training.data,]}

```







####Saving both files as csv files.

#####Testing dataset;
```{r}


write.csv(test.data,file = "test.data.csv")      #####testing dataset
read.csv("test.data.csv")
```







#####Training dataset;

```{r}



write.csv(train.data,file="train.data.csv")
read.csv("train.data.csv")                       #####training dataset




```






####Finding the no.of USA and non-USA cars in the training Dataset.
```{r}

usa <- train.data[train.data$Origin=="USA",]
nrow(usa)

non.usa <- train.data[train.data$Origin=="non-USA",]
nrow(non.usa)

```




###Q2.
#####(a),sampling 10 births and 10000 births given probability.
```{r}

#####10 births
set.seed(2)
bg.10 <- sample(c("boy","girl"),10,prob = c(0.515,0.485),replace = TRUE)
table(bg.10)


                                

#####10,000 births
set.seed(3)
bg.10000 <- sample(c("boy","girl"),10000,prob = c(0.515,0.485),replace = TRUE)
table(bg.10000)
```






###Q3:Binomial distribution:


####probability of having exactly 3 boys:

```{r}

    dbinom(3,size = 10,prob = 0.515)       ####  p(x=3),size=10
    ```


####probability of having 8 or more boys out of 10 births.
```{r}
  1-pbinom(7,size = 10,prob = 0.515) 
```









####density function of the no.of boy births out of 10

```{r}
n <- 10
x <- 0:n
y <- dbinom(x,size = 10,prob = 0.515)
plot(x,y,main = "Density function plot",xlab = "No. of boy births",ylab = "Probability",col="green",type = "b")
```






####cumulative function of the no. of boys out of 10 births
```{r}
n <- 10
x <- 0:n
y <- pbinom(x,size = 10,prob = 0.515)
library(ggplot2)
plot(x,y,main = "Cumulative probability function plot",xlab = "No. of boy births",ylab = "Probability",col="green",type = "b")
```


###Q4
###Poisson Distribution.

```{r, message=FALSE, warning=FALSE}

####probability that exactly 4 cars arrive in the next 10 sec;(x=4)

dpois(4,lambda = 5)




####probability that more than 5 cars arrive in the next 10 sec;(x>5)
ppois(5,lambda = 5,lower.tail = FALSE)


#####plot density function of 0-20 cars arriving in the next 10 sec

n <- 20
x <- 0:n
y <- dpois(x,lambda = 5)

plot(x,y,main = "Density function plot",xlab = "No.of cars",ylab = "Average time",col="blue",type = "b")
```