Winnie.Rmd

---
title: "Lab  4"
author: "Winnie Ngare"
output:
  html_document:
    toc: yes
  html_notebook:
    toc: yes
    toc_float: yes
---

```{r setup, include=FALSE}
knitr::opts_chunk$set(echo = TRUE)
```


##Qn 1:Normal distribution.
###No. of points(x) in a tournament are **normally distributed with a **mean =32 & sd=7
### 20 points or fewer(x<=20)
```{r}
pnorm(20,mean = 32,sd=7)
#####Density function.
curve(dnorm(x,mean = 32,sd=7),from = 11, to=53)
norm.x <- c(11,seq(11,20,by=0.01),20)
norm.y <- c(0,dnorm(seq(11,20,0.01),mean = 32,sd=7),0)
polygon(norm.x,norm.y,col = "blue")
```






###b)more than 35 points.
```{r}
####More than 35 points.
pnorm(35,mean = 32,sd=7,lower.tail = FALSE)

####density function
curve(dnorm(x,mean = 32,sd=7),from = 11, to=53)
x.cord <- c(35,seq(35,53,0.01),53)
y.cord <- c(0,dnorm(seq(35,53,0.01),mean = 32,sd=7),0)
polygon(x.cord,y.cord,col = "blue")
```







###c)Team scoring between 20 and 40 points.
```{r}

pnorm(40,mean = 32,sd=7)-pnorm(20,mean = 32,sd=7)


####density function 
curve(dnorm(x,mean = 32,sd=7),from=11,to=53)
x <- c(20,seq(20,40,0.01),40)
y <- c(0,dnorm(seq(20,40,0.01),mean = 32,sd=7),0)
polygon(x,y,col = "blue")
```







##Q2;Exponential distribution.
###a)Fewer than 3 comments;
```{r, warning=FALSE}
pexp(3,0.1)   ####25.91% get less than 3 comments
```






###density function
```{r, message=FALSE, warning=FALSE}
curve(dexp(x,0.1),from=0,to=90)
x <- c(0,seq(0, 3, 0.1),3)
y <- c(0,dexp(seq(0, 3, 0.1), 0.1),0)
polygon(x,y,col = "blue")
```









###b)more than 20 comments
```{r, message=FALSE, warning=FALSE}
pexp(20,0.1,lower.tail = FALSE)     ####13.53% get more than 20 comments.

curve(dexp(x,0.1),from=0,to=90)
x <- c(20,seq(20,90,0.1),90)
y <- c(0,dexp(seq(20,90,0.1),0.1),0)
polygon(x,y,col = "blue")
```








###C)between 5 and 10 comments
```{r}
pexp(10,0.1)-pexp(5,0.1)       #### 23.86% get between 5 and 10 comments.

curve(dexp(x,0.1),from=0,to=90)
x <- c(5,seq(5,10,0.1),10)
y <- c(0,dexp(seq(5,10,0.1),0.1),0)
polygon(x,y,col = "blue")
```








##Q3; Basic Raster creation and calculation:
###Raster of runif distribution.(30*30)
```{r, message=FALSE, warning=FALSE}

library(raster)
ras1 <- raster(nrows=30,ncols=30,xmn=0,xmx=30,ymn=0,ymx=30)
ras1
set.seed(10)
ras1[] <- runif(ncell(ras1))


plot(ras1)
hist(ras1)
```










###raster of a rnorm distribution.(30*30)
```{r}
ras2 <- raster(nrows=30,ncols=30,xmn=0,xmx=30,ymn=0,ymx=30)
ras2
set.seed(100)
ras2[] <- rnorm(ncell(ras2))
plot(ras2)
hist(ras2)

```











###third raster(additional)
```{r}
ras.add <- ras1+ ras2
ras.add
plot(ras.add)
hist(ras.add)

```










###Mean of third raster.
```{r}
rasmean <- cellStats(ras.add,"mean")
rasmean
```










###reclassifying 3rd raster and saving it to the directory.
```{r, message=FALSE, warning=FALSE}
library(rgdal)
ras.add[ras.add>rasmean] <- 1
ras.add[ras.add <=rasmean] <- 0
plot(ras.add)
hist(ras.add)
writeRaster(ras.add, filename = "thirdraster.tif", overwrite=T)
read=raster("thirdraster.tif")


```