Hey gfbrd.
Given your constraints you will never get a solution since your maximum value will be 7+7+7=21 and your minimum will be 3+3+3=9. Did you mean to say something else?
Edit: Can't add up properly.
Hey there everyone, I need some help with this math problem, hoping to get some help on this topic.
Use generating functions to find the number of solutions in integers to the equation a+b+c=30 where each variable is at least 3 and at most 7.
Please explain to me step by step on how to do this so I can understand it better thanks.
Hey gfbrd.
Given your constraints you will never get a solution since your maximum value will be 7+7+7=21 and your minimum will be 3+3+3=9. Did you mean to say something else?
Edit: Can't add up properly.
Thanks for pointing out the error.
Well it sounds like what they want you to do is have two independent random variables with 3 to 7 and then have another random variable which is 30 minus the sum of those two.
The sum of two random variables' distribution can be found with a PGF and this will be based on two uniform distributions of 5 values with same probability for 3 to 7 inclusive.
Then the other variable will be 30 - (X+Y) but 30 is just a special case of a distribution where you have Z - W where Z has a probability density function of P(Z=30) = 1 and the distribution of -W just reflects the distribution around the y-axis.
So can you calculate for a start the PGF for the sum of two uniform random variables (discrete uniform) with values going from 3 to 7 inclusive.