- #1
deltapants
- 5
- 0
First of all,
THIS IS NOT HOMEWORK. It's related to my research.
And forgive me if this is rather elementary (sadly, I was something of an underachiever at school, which has left some gaps in my maths education that I've been working on since I returned to education) but I have a question about estimating the fraction of spalled impact ejecta that occupies a given velocity range. I have a reasonable estimate for the total number of particles ejected, and a minimum and maximum velocity (11.2 and 15).
I'm assuming that the ejecta follows a Gaussian distribution, and I'm assuming a variance of 1 and a mean of 13.1.
My question is - how would I actually integrate this, so I can estimate how many particles are traveling between 11.7 and 12.7 km/s?
I've been approaching the problem conceptually like I might with a QM problem, by considering the function as a probability distribution such that the integral between -∞ and +∞ = 1, except in this case it's between 11.2 and 15 as my limits. Does this make sense? How would I then go about integrating between the 11.7 and 12.7 limits? Do I set 11.2 = 0 and 15 = 1 or something?
Again, sorry if this is all very elementary, but some guidance would be appreciated!
THIS IS NOT HOMEWORK. It's related to my research.
And forgive me if this is rather elementary (sadly, I was something of an underachiever at school, which has left some gaps in my maths education that I've been working on since I returned to education) but I have a question about estimating the fraction of spalled impact ejecta that occupies a given velocity range. I have a reasonable estimate for the total number of particles ejected, and a minimum and maximum velocity (11.2 and 15).
I'm assuming that the ejecta follows a Gaussian distribution, and I'm assuming a variance of 1 and a mean of 13.1.
My question is - how would I actually integrate this, so I can estimate how many particles are traveling between 11.7 and 12.7 km/s?
I've been approaching the problem conceptually like I might with a QM problem, by considering the function as a probability distribution such that the integral between -∞ and +∞ = 1, except in this case it's between 11.2 and 15 as my limits. Does this make sense? How would I then go about integrating between the 11.7 and 12.7 limits? Do I set 11.2 = 0 and 15 = 1 or something?
Again, sorry if this is all very elementary, but some guidance would be appreciated!