

FlashChat  Actuarial Discussion  Preliminary Exams  CAS/SOA Exams  Cyberchat  Around the World  Suggestions 
DW Simpson Global Actuarial & Analytics Recruitment 
Probability Old Exam P Forum 

Thread Tools  Search this Thread  Display Modes 
#3




Note that your method only works perfectly if the function is one to one.... Note cos(x) is not one to one over the interval [0,2pi] so you need to multiple by a constant.....To figure out the constant, it might be more intuitive to solve pdf transformations of non onetoone functions using the CDF method.... drawing a picture might help.... this problem however is a common transformation and you can memorize to multiple it by 2 over the interval.

#4




Thank you for the response. I think I understand what you are explaining. Because the inverse of f(x) range and domain do not match with a 1 to 1, but rather 1 to 2, then the solution is doubled. Aside from trigonometric identities and square transformation, ( Y=X^2), what other problems will have non 1 to 1 relations?
Now I understand why I was missing so many of these problems. Looks like the range of the original function will also determine where to consider the negative value of the square in the inverse. I spend days hitting my head against a wall trying to figure out this stuff.  There is new crack in the wall today. Last edited by jchaney; 09212016 at 03:09 PM.. 
#5




Quote:

Thread Tools  Search this Thread 
Display Modes  

