According to probability theory, if two random variables each follow an Exponential distribution with rates a and b, respectively, then their minimum is also an Exponential random variable with rate a+b. how can I prove this using R ? using the below rates for a and b?

a

0.1

0.2

0.3

0.4

0.5

0.6

b

0.3

0.7

0.8

0.9

1.0

1.5