$$X_{1}$$ and $$X_{2}$$ represent number of occurrences of event A and 8 that follow Poisson distribution with mean rate $$\lambda_{1}$$ and $$\lambda_{2}$$, If $$Y_{1}$$ and $$Y_{2}$$ are inter-occurrence times of event A and B, then min($$Y_{1},Y_{2}$$) follows

A

Exponential distribution with mean rate min ($$\lambda_{1}, \lambda_{2}$$)

B

Exponential distribution with mean rate ($$\lambda_{1} + \lambda_{2}$$)

C

Poisson distribution with mean rate ($$\lambda_{1} - \lambda_{2}$$)

D

Poisson distribution with mean rate ($$\lambda_{1} + \lambda_{2}$$)