```
# We simulate 100000 trials for selection of number B from the interval 0 to 1, with equal probability of each outcome
B<-runif(100000, min=0, max=1)
```

```
# We check the minimum and maximum values for the number B
min(B)
```

`## [1] 1.081359e-05`

`max(B)`

`## [1] 0.9999895`

We see that all the values are non-zero

`hist(B, probability = TRUE)`

The histogram of values of B shows that the density of all values adds up to 1. So both the conditions of a probability distribution are satisfied. The function is positive everywhere and the cumulative values add up to 1.

We repeat the same calculations for function C and arrive at the same conclusion as well.

```
C<-runif(100000, min=0, max=1)
min(C)
```

`## [1] 1.039822e-06`

`max(C)`

`## [1] 0.9999814`

`hist(C, probability = TRUE)`

- B + C < 1/2
- BC < 1/2
- |B ??? C| < 1/2
- max{B,C} < 1/2
- min{B,C} < 1/2

```
compound1<-B+C
sum((compound1)<.5)/100000
```

`## [1] 0.12516`

```
compound2<-B*C
sum((compound2)<.5)/100000
```

`## [1] 0.84705`

```
compound3<-abs(B-C)
sum((compound3)<.5)/100000
```

`## [1] 0.75099`

```
compound4<-pmax(B,C)
sum((compound4)<.5)/100000
```

`## [1] 0.25041`

```
compound5<-pmin(B,C)
sum((compound5)<.5)/100000
```

`## [1] 0.7509`