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I am having trouble with the concept of joint pdf's. For example - a set Z1,Z2,...ZN are each gaussian rv.

Let Z1~N(0,1), let X be +1 or -1 each with probability 0.5. Z2=Z1X1, so Z2 is ~N(0,1).

(I assume this to be As Z2 is just Z1 multiplied by a simple factor, an instance of X, either +1 or -1.)

I am having trouble understanding how the joint pdf pZ1Z2(z1,z2) is impulsive on the diagnols where z2=+/-z1 and is zero elsewhere.

I can understand how the joint pdf of for example pZ1X(z1,x) would be zero but impulsive on the diagnols but not when the joint pdf is made from the two gaussians as described - - advice appreciated