1. The problem statement, all variables and given/known data

1.

Suppose u flip a coin

Z = 1 if the coin is heads

Z = 3 if the coin is tails

W = Z^2 + Z

a)

what is the probability function of Z?

b)

what is the probability function of W?

2.

Let Z ~ Geometric (theta). Compute P(5<=Z<=9).

2. Relevant equations

3. The attempt at a solution

1.

what i think

a)

Pz(Z) = 1 if head

3 if tail

0 otherwise

b)

Pw(W) = 2 if head

12 if tail

0 otherwise

I don't see how the probability part comes into this, where do i include the 1/2 chance part...

or maybe its:

a)

Pz(Z) = 1/2 if Z is 1 or 3

0 otherwise

b)

Pw(W) = 1/2 if W is 2 or 12

0 otherwise

2.