Question

Find the probability that none of three bulbs in a traffic signal will have to be replaced during the first 1500 hours of operation if the lifetime X of a bulb is a randomvariable b with density f(b) = 6(0.25 – (b - 2.5)2) when 1< b < 2 and 0 otherwise,

Answer 1

=1- P(x<=2.4)^3
=1-F(2.4)^3
=1-int from(2 to x)of 6(0.25-(t-2.5)^2)dt)^3, @x=2.4
=1-(6(0.25)(x-2)-(x-2.5)^3-(-0.5)^3)/3)^3