X and Y are investment returns which are normally distributed with X~N(1000,250) Y~N(1000,250) for two consecutive years. The tax rates for year 1 is 30%. The tax rate for year 2 is 20%. If there are losses the taxes on the losses are returned. What is the probability that the total return is positive after two years.
I am trying to solve as follows:
1> x >0, y>0 return positive after two years.
2> x <0, y>0.7x (because 0.3x is returned) return positive after two years.
3> x >0.8y, y<0 (because 0.2y is returned) return positive after two years.
After this I fail to integrate properly for possibility 2 and 3.
Can someone please help me to figure out if there is a nice way to integrate or solve the above problem.
Thanks in advance