2
$\begingroup$

A is fighting against B. Suppose A's attacks (which all hit) represent a Poisson process with intensity $\lambda = 1/6$. B, on the other side, needs 4 seconds to load and launch his attack, but when he's hit, the timer is reset.

Which is the mean length of the time intervals between two A attacks in which B has attacked at least once?

Here is my attempt:

Let $X$ be the number of arrivals of $A$ in $[0,t)$. Then $X$ ~ $\text{Poisson}(\mu = t/6)$.

I want $P(X\ge 1) = 0.5$. $$P(X\ge 1) = 1- P(x=0) =1-e^{-t/6}=0.5$$ Therefore $t=4.158$ seconds. I'm not really sure about that. I tried calculating $E(Y=1|X=0)$, where $Y$ is the number of arrivals of $B$ but the solution doesn't make any sense.

  • 0
    "I want $P(X\ge 1) = 0.5$" No idea why you would want that to solve the question. Please explain. – 2017-02-05
  • 0
    Assuming A already attacked once, I wanted to calculate the average time A attacks again and i thought 50% is the average of it – 2017-02-05

0 Answers 0