The lifetime X of a bulb is a random variable with the probability density function:

f(x)={ 6[0.25-(X-1.5)^2] when 1<=X<=2
f(x)={ 0 Otherwise
X is measured in multiples of 1000 hrs. What is the probability that none of the three
bulbs in a traffic signal have to be replaced in the first 1500 hrs of their operation.