- #1
LucasGB
- 181
- 0
Hello,
Suppose you observe some foam. The foam is formed by a set of bubbles, and each bubble blows up after a random time. The density function of the time each bubble will take to blow up is probably exponential, with rate lambda. The total amount of foam (Q) must also decay exponentially, at a rate given by the decay constant beta.
So, we have to exponencial functions:
1) the exponencial density function that determines the lifetime of each individual buble:
f(t) = lambda*exp(-lambda*t)
2) the exponencial decay that determines the amount of foam we have at time t:
Q(t)=Q[0]*exp(-beta*t)
The relation between these two functions is not clear to me. What is the relation between lambda and beta?
Thanks in advance,
Estêvão
Suppose you observe some foam. The foam is formed by a set of bubbles, and each bubble blows up after a random time. The density function of the time each bubble will take to blow up is probably exponential, with rate lambda. The total amount of foam (Q) must also decay exponentially, at a rate given by the decay constant beta.
So, we have to exponencial functions:
1) the exponencial density function that determines the lifetime of each individual buble:
f(t) = lambda*exp(-lambda*t)
2) the exponencial decay that determines the amount of foam we have at time t:
Q(t)=Q[0]*exp(-beta*t)
The relation between these two functions is not clear to me. What is the relation between lambda and beta?
Thanks in advance,
Estêvão