if X1 and X2 are independent random variables from the standard normal distribution i have worked out the joint probability density function of X1,X2 to be

(1/2π) exp[-1(x12 + x22 ) /2 ] (is this correct?)

then if Y1=X1 and Y2=X2/X1 the joint probability density function of Y1,Y2 is

(1/2π) exp[-1y12 (1+y22)/2) ] |J|

i worked out J to be y1

is that all correct and what does the joint probability density function of Y1, Y2 then become?

thanks