You arrive at a bus stop at 10 o’clock, knowing that the bus will arri

puntgewelb5

puntgewelb5

Answered question

2021-11-14

You arrive at a bus stop at 10 o’clock, knowing that the bus will arrive at some time uniformly distributed between 10 and 10:30. (a) What is the probability that you will have to wait longer than 10 minutes? (b) If, at 10:15, the bus has not yet arrived, what is the probability that you will have to wait at least an additional 10 minutes?

Answer & Explanation

Alicia Washington

Alicia Washington

Beginner2021-11-15Added 23 answers

Given that Bus arrives uniformly at the bus stop between 10am and 10:30am
Let X denote the arrival of bus at the bus stop. Then, X is a uniform random variable having density as
f(x)=130;x[0,30]
a) Probability that a passenger arriving at the bus stop between 10 and 10:30 will have to wait more than 10 minutes.
P[X>10]=1030f(x)dx=1030130dx=130[x]1030=130[3010]=2030=23
b) At 10:15am, bus hasnt

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