Question

Suppose that appearances of a foe to battle (that is, a random encounter) in a role-playing game occur according to a Poisson process, and the average rate equals one appearance per two minutes. Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?

Answer 1

Rate parameter of
`\mu = 0.5`

Explanation:

Exponential distribution:

The exponential probability distribution, with mean m, is described by the following equation:

`f(x) = \mu e^(-\mu x)`

In which
`\mu = (1)/(m)` is the decay parameter.

One appearance per two minutes.

This means that
`m = 2`

Measured in minutes, the time T until the next encounter is Exponential with what rate parameter?

`\mu = (1)/(m) = (1)/(2) = 0.5`

So

Rate parameter of
`\mu = 0.5`