Suppose a stop light is alternately green and red, with each color lasting five

Question

Suppose a stop light is alternately green and red, with each color lasting five minutes. Suppose also that the time at which motorists arrive at the stop light 24 is uniformly distributed over the ten minute green-red cycle. Let W be the time a randomly chosen motorist waits at the the stop light. Then the random variable W is neither discrete nor continuous.

Let W be the time a motorist waits at the light in our example exhibiting a random variable which is neither discrete nor continuous. Find the associated cumulative distribution function

Explanation / Answer

Given: W is uniform on [0,10] if the motorists is equally likely to arrive at any time in the range of o to 10 minute green-red cycle.
f(w) = 1/10 for 0 w 10 and f(w) = 0 for all other values.
CDF:
P(W w) = F(w) (On integrating f(w) from -inf to t)

F(w) = (w / 10) for 0 w 10 , F(w) = 0 for w < 0 and F(w) = 1 for w > 10

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