When an emergency occurs, the response time (in hours) of the first police car is a random variable X with density
fx(x) = I2e-12x
for x > 0,
and fX (x) = 0 otherwise. The response time (in hours) of the first fire engine is a random variable Y with density
fY(y) = 10e-10y
for y > 0,
and fY(y) = 0 otherwise. Assume X and Y are independent.
Find the probability that the first police car arrives before the first fire engine.