Probability mass function of derived random variables from coin flip

[sneaky666]

Homework Statement

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).

Homework Equations

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.

 

[vela]

One of the important things you need to do in math is be precise with your notation. Tell us what is P_Z(z) supposed to represent? That's where some of your confusion lies.