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## Homework Statement

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Driving to work, a commuter passes through a sequence of three traffic lights. At each light he either stops, denoted by s, or continues, denoted by c. Assume that the outcome c or s for each traffic light is independent of the outcome of other traffic lights.

(a) Write out the sample space Ω.

(b) If X(ω) is the number of times the commuter stops for outcome ω, calculate X for each outcome in your sample space and write out the state space S for X.

(c) Assuming that each outcome ω is equally likely, calculate the PMF fX of X, with reasoning.

(d) Assuming that stopping at a light is twice as likely as continuing through, calculate the PMF fX of X.

## The Attempt at a Solution

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A)

Ω={ccc,ccs,css,sss,ssc,scc,csc,scs}

b)

x(ccc)=0

x(ccs)=1=x(csc)=x(scc)

x(css)=2=x(ssc)=x(scs)

x(sss)=3

state space ={0,1,2,3}

c)

wouldn't the pmf just be this but the questions says equally likely.

p(X=0)=1/8

p(X=1)=3/8

p(X=2)=3/8

p(X=3)=1/8

d)

not sure how to go about this part