Help please

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Help please
Message posted by Sabrina on November 21, 2000 at 12:00 AM (ET)

Toss a coin 5 times. Let X= #of heads; Y= #of tails. Define Z=X+Y and W as the product of V=XY. What is the joint pdf of (Z,V)? Are Z,V independent random variables?

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Re: Help please
Message posted by Phil on November 22, 2000 at 12:00 AM (ET)

Z=X+Y will always be 5. Since knowing W has no effect on what Z is, they are independent.

The values of W are limited to 0, 4, and 6 with probabilities 1/16, 5/16, and 10/16 respectively (binomial).

The Joint pdf is trivial since Z has only one value, 5.

This question was designed to see if you understood the material.

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