Mathematics, 02.11.2019 04:31, woodsjnjoseph3
Abus arrives at a bus stop at a uniformly distributed time over the interval 0 to 1 hour. a passenger also arrives at the bus stop at a uniformly distributed time over the interval 0 to 1 hour. assume that the arrival times of the bus and passenger are independent of one another and that the passenger will wait for up to 1/4 hour for the bus to arrive. what is the probability that the passenger will catch the bus?
Answers: 2
![P( y < x < y+\frac{1}{4})\\\\=\displaystyle\int_0^1\int_{y}^{y+\frac{1}{4}} f(x,y) dxdy\\\\=\displaystyle\int_{0}^{1} [y]_{y}^{y+\frac{1}{4}} dx= \int_0^1 \frac{1}{4}dx = \frac{1}{4} = 0.25](/tpl/images/0356/4435/425c9.png)
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