1. Probabilities from Distribution Functions

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)?

2. Re: Probabilities from Distribution Functions

Hi! We are glad that you posted here! This looks like a homework question though. Our homework help policy can be found here. We mainly just want to see what you have tried so far and that you have put some effort into the problem. I would also suggest checking out this thread for some guidelines on smart posting behavior that can help you get answers that are better much more quickly.

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