STA 326 2.0 Programming and Data Analysis with R

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# STA 326 2.0 Programming and Data Analysis with R
## Lesson 5.1: Recap-Functions
### Dr Thiyanga Talagala
### 2020-03-10

---

# Problem 1

Write a function to prints out standard random normal numbers (use rnorm()) but stops (breaks) if you get a number bigger than 1.

Using next adapt the loop from last exercise so that doesn’t print negative numbers.

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# Problem 2

Write a function to simulate the flip a coin `$n$` times, keeping track of the individual outcomes (1 = heads, 0 = tails) in a vector that
you preallocte. Assume `$P(H)=0.5$`.

Example output:

```r
flip_coin(10)
```

```
 [1] "H" "T" "T" "H" "H" "H" "H" "H" "T" "T"
```

---

```r
flip_coin <- function(n){
  out <- numeric(n)
  for (i in 1:n){
    coin.out <- rbinom(1, p=0.5, n=1)
    if(coin.out==1){
      out[i] <- "H"
    } else {
      out[i] <- "T"
    }
  }
  out
}
```

```r
flip_coin(10)
```

```
 [1] "T" "T" "H" "H" "H" "T" "H" "T" "T" "T"
```

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- Modify the function so that it takes another argument, which will be the `$P(H)$`.

- Run the function 10, 100, 1000 and 10000 times with `$P(H)=0.8$` and report the proportion of times that head is selected.

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# Problem 3

Write a function to calculate the median.

help:

```r
5%%2
```

```
[1] 1
```

```r
4%%2
```

```
[1] 0
```

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# Problem 4

Write a function to calculate the correlation coefficient

`$$r=\frac{\sum_{i=1}^{n}(x_i-\bar{x})(y_i-\bar{y})}{\sqrt{\sum_{i=1}^n(x_i-\bar{x})^2\sum_{i=1}^n(y_i-\bar{y})^2}}$$`

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