# Task 1 {#1}

## Wait - how do I even run things in Julia/VScode?
Typically, you work in a Julia script ending in `scriptname.jl`

You concurrently have a REPL open, to not reload all packages etc. everytime. Further you typically have `Revise.jl` running in the background to automatically update your custom Packages / Modules (more to that later).

You can mark some code and execute it using `ctrl` + `enter` - you can also generate code-blocks using `#---` and run a whole code-block using `alt`+`enter`

## The exercise
1. Open a new script `statistic_functions.jl` in VSCode in a folder of your choice.

2. implement a function called `rse_sum`^[rse = research software engineering, we could use `sum` in a principled way, but it requires some knowledge you likely don't have right now]. This function should return `true` if provided with the following test: `rse_sum(1:36) == 666`. You should further make use of a for-loop.

3. implement a second function called `rse_mean`, which calculates the mean of the provided vector. Make sure to use the `rse_sum` function! Test it using `rse_mean(-15:17) == 1`

4. Next implement a standard deviation function `rse_std`: $\sqrt{\frac{\sum((x-mean(x))^2)}{n-1}}$, this time you should use elementwise/broadcasting operators. Test it with `rse_std(1:3) == 1.`

5. Finally, we will implement `rse_tstat`, returning the t-value with `length(x)-1` DF, that the provided Array actually has a mean of 0. The formula is $\frac{mean(x)}{std(x) / (sqrt(length(x)))}$ Test it with `rse_tstat(2:3) == 5.`. Add the keyword argument `σ` that allows the user to optionally provide a pre-calculated standard deviation. 

Well done! You now have all functions defined with which we will continue our journey.

::: callout
## Bonus Task ProgressMeter
for very large sums we might want to add a progressmeter. To do so:

```julia
]add ProgressMeter
using ProgressMeter
...
@showprogress for ...
```

:::

And that's it! You should have a nice progress bar now


# Task 2 {#2}

1. Implement a type `StatResult` with fields for `x`, `n`, `std` and `tvalue`
2. Implement an outer constructor that can run `StatResult(2:10)` and return the full type including the calculated t-values.
3. Implement a function length for StatResult (using multiple-dispatch) which returns the `.n` field. Overload "Base.length"
4. **Optional:** If you have time, optimize the functions, so that mean, sum, length, std etc. is not calculated multiple times - you might want to rewrite your type. Note: This is a bit tricky :)

