# Issue to solve this proof

Probability theory and statistics

### Issue to solve this proof

Good morning.

My problem is as follow:

I have an event assuming A. The probability that A occurs at time t is: $p(t)= e^{-bt}*|sin(at)|$. Where a,b are positive parameters

We divide the time in small step times let's say $\delta t= 0.125$, Then, we count how many time A occur for $t =[0, \infty]$.

So my problem is to study the number of occurrence of A in the variation of the parameter a and b.
Which I can prove mathematically that for a lower value of b, A occurs more often and for the bigger value of a, A occurs more frequently.

I hope I was clear.
If anyone has any suggestion or idea about how could we do that.
Thank you.

Guest