## A random integer from min to max

Create a function `randomInteger(min, max)`

that generates a random *integer* number from `min`

to `max`

including both `min`

and `max`

as possible values.

Any number from the interval `min..max`

must appear with the same probability.

Examples of its work:

```
alert( random(1, 5) ); // 1
alert( random(1, 5) ); // 3
alert( random(1, 5) ); // 5
```

#### The simple but wrong solution

The simplest, but wrong solution would be to generate a value from `min`

to `max`

and round it:

```
function randomInteger(min, max) {
let rand = min + Math.random() * (max - min);
return Math.round(rand);
}
alert( randomInteger(1, 3) );
```

The function works, but it is incorrect. The probability to get edge values `min`

and `max`

is two times less than any other.

If you run the example above many times, you would easily see that `2`

appears the most often.

That happens because `Math.round()`

gets random numbers from the interval `1..3`

and rounds them as follows:

```
values from 1 ... to 1.4999999999 become 1
values from 1.5 ... to 2.4999999999 become 2
values from 2.5 ... to 2.9999999999 become 3
```

Now we can clearly see that `1`

gets twice less values than `2`

. And the same with `3`

.

#### The correct solution

There are many correct solutions to the task. One of them is to adjust interval borders. To ensure the same intervals, we can generate values from `0.5 to 2.5`

, thus adding the required probabilities to the edges:

```
function randomInteger(min, max) {
// now rand is from (min-0.5) to (max+0.5)
let rand = min - 0.5 + Math.random() * (max - min + 1);
return Math.round(rand);
}
alert( randomInteger(1, 3) );
```

An alternative way could be to use `Math.floor`

for a random number from `min`

to `max+1`

:

```
function randomInteger(min, max) {
// here rand is from min to (max+1)
let rand = min + Math.random() * (max + 1 - min);
return Math.floor(rand);
}
alert( randomInteger(1, 3) );
```

Now all intervals are mapped this way:

```
values from 1 ... to 1.9999999999 become 1
values from 2 ... to 2.9999999999 become 2
values from 3 ... to 3.9999999999 become 3
```

All intervals have the same length, making the final distribution uniform.