Determining the time interval in a radiation counting problem

[SKT_90]

Homework Statement

Given: Cn_dot = true event rate = 10 interactions/s
p(t')dt' = differential probability of an event

Homework Equations

p(t')dt' = Cn_dot * exp(-Cn_dot * t') dt'

The Attempt at a Solution

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I want to sample the time interval using python. But I'm not sure how to go about manipulating the formula to get t.

Should I integrate both sides from 0 to x and isolate for t? I'm not sure what to make of the LHS.

 

[mfb]

What do you mean by "to get t"?
What do you want to do?

 

[scottdave]

What do you mean by "to get t"?
What do you want to do?

I think if this is to be run through a program, then a suitable value for Δt should be chosen. Is that what you mean @SKT_90 ?
Also, what is the significance of t prime, vs just t?
It looks to me that if you integrate it from 0 to time T, you will have a probability function that it happens in T seconds.

 

[SKT_90]

I think if this is to be run through a program, then a suitable value for Δt should be chosen. Is that what you mean @SKT_90 ?
Also, what is the significance of t prime, vs just t?
It looks to me that if you integrate it from 0 to time T, you will have a probability function that it happens in T seconds.

Hi scottdave,

Yes - this is what I mean to do. I think t' is just a dummy variable as stated in the question, so we can integrate it from 0 to t.

 

[SKT_90]

So i get :

1 - exp(-Cn_dot * t) = p(t)

I'm not sure how to sample the time from here?

 

[SKT_90]

nvm, figured it out