Z can be equal to 1 or 3.
The probability distribution function of Z will tell you what is the probability that Z takes each of these 2 values.
So P(Z=1) =P(outcome is head)=1/2
and P(Z=2)=P(outcome is tail)=1/2
Similar reasoning applies to W.
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.