Can we say that kX and Y are independent RVs for any real constant k?

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- Oct 12th 2013, 02:15 PMJameIf X and Y are independent RVs...
Can we say that kX and Y are independent RVs for any real constant k?

- Oct 12th 2013, 04:59 PMchiroRe: If X and Y are independent RVs...
Hey Jame.

The answer is yes. You can prove this by showing that if Z = kX, then the PDF P(Z = z, Y = y) = P(Z=z)*P(Y=y). As long as you can show this separable property, you will always be able to show independence.