1. ## bivariate probability question

two buses, A and B, operate on a route. A person arrives at a bus stop on this route at time 0. Let X and Y be the arrival times of bus A and bus B respectively, at this stop afterward. Suppose that X and Y are independent and have the density functions, respectively, by:

f1(x) = 1/a, if 0<x<a
0 otherwise

f2(y) = 1/b, if 0<y<b
0 otherwise

where a,b>0 are constants. what is the probablity that bus B will arrive before bus A?

THANKS

2. Originally Posted by lauren2988
two buses, A and B, operate on a route. A person arrives at a bus stop on this route at time 0. Let X and Y be the arrival times of bus A and bus B respectively, at this stop afterward. Suppose that X and Y are independent and have the density functions, respectively, by:

f1(x) = 1/a, if 0<x<a
0 otherwise

f2(y) = 1/b, if 0<y<b
0 otherwise

where a,b>0 are constants. what is the probablity that bus B will arrive before bus A?

THANKS
$g(x, y) = f_1(x) \cdot f_2(y) = \frac{1}{ab}$ where $0 < x < a$ and $0 < y < b$.

The answer is therefore $\frac{1}{ab} \cdot {R_{xy}}$ where $R_{xy}$ is the area that lies above the line $y = x$ that is enclosed by the axes and the lines $x = a$ and $y = b$ (this will depend on whether a > b or a < b and can be fuond using geometry - draw a diagram).