Let X,Y,ZX, Y, ZX,Y,Z be independent with X∼N(0,1),Y∼χ22,Z∼χ32X \sim N(0,1), Y \sim \chi^2_2, Z \sim \chi^2_3X∼N(0,1),Y∼χ22,Z∼χ32. What is the distribution of X(Y+Z)/5\frac{X}{\sqrt{(Y+Z)/5}}(Y+Z)/5X?
t5t_5t5
t2t_2t2
t3t_3t3
N(0,1)N(0,1)N(0,1)