Buses arrive at ﬁfteen minute intervals starting at noon. Anne arrives at the bus stop X minutes after noon, where X is a random variable with distribution function

FX(x) = P(X ≤ x) = 0 for x < 0,

x2 /3600 for 0 ≤ x ≤ 60,

1 for x > 60.

(a) What is the probability that Anne waits less than ﬁve minutes for a bus?

(b) What is the probability that Anne waits more than ten minutes for a bus?

(c) Is Anne more likely to arrive before 12.30 pm or after 12.30 pm? Is Anne’s arrival time, X, ‘uniformly distributed’ on the interval [0, 60]? Give reasons for your answer.

Any help or solutions for this problem would be greatly appreciated.

For a) I was thinking it would be FX(5) but the questions asks for the chance she waits less than 5 minutes and I thought that FX(5) would be less than or equal to 5?

Same problem for b) although I was thinking maybe 1- FX(10)?

FX(x) = P(X ≤ x) = 0 for x < 0,

x2 /3600 for 0 ≤ x ≤ 60,

1 for x > 60.

(a) What is the probability that Anne waits less than ﬁve minutes for a bus?

(b) What is the probability that Anne waits more than ten minutes for a bus?

(c) Is Anne more likely to arrive before 12.30 pm or after 12.30 pm? Is Anne’s arrival time, X, ‘uniformly distributed’ on the interval [0, 60]? Give reasons for your answer.

Any help or solutions for this problem would be greatly appreciated.

For a) I was thinking it would be FX(5) but the questions asks for the chance she waits less than 5 minutes and I thought that FX(5) would be less than or equal to 5?

Same problem for b) although I was thinking maybe 1- FX(10)?

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