Let X1, X2, X3, be random variables (assume independance) with values 1 and 3 and have probability 1/2
Suppose Y1 = X2 x X3 + X1 and Y2 = X1 x X2 - X3
Calculate the joint probability density function fx,y (y1,y2) also the mean, variance and covariance, marginal pdf of (y1,y2)
also conditional distribution and conditional mean of Y1 given Y2=0
Its the first part that I struggle with the most, im just really not sure what its suppose to mean, do all the variables X1, X2, X3 have probabilty 1/2? does that mean Y1 = 1 and Y2 = -0.25?
also what does the 'with values 1 and 3 bit mean?'
I dont know what to make of the joint p.d.f either, f(x,y) (xj,yj) = P(X=xj,Y=yj) and the marginal pdf looks scary from here but im sure will make more sence once I get a handle on things.