Suppose that the probability distribution function for the life expectancy of a light bulb is given below. If a lamp has two light bulbs, what is the probability that they will both fail within the first 1000 hours (Hint: Assume one light bulb is X and the other Y. Since X and Yare independent events, assume,f(x,y)-NX)从Y ) where f-f.-f, then use problem #4 from Written Assignment #7 as a guide for the anti-differentiation.) f(x)=-1 е-(X-1000,2/125000 250 y2r Suppose that the probability distribution function for the life expectancy of a light bulb is given below. If a lamp has two light bulbs, what is the probability that they will both fail within the first 1000 hours (Hint: Assume one light bulb is X and the other Y. Since X and Yare independent events, assume,f(x,y)-NX)从Y ) where f-f.-f, then use problem #4 from Written Assignment #7 as a guide for the anti-differentiation.) f(x)=-1 е-(X-1000,2/125000 250 y2r