Let T represent the useful lifetime / time to failure of a LED lights produced by ABC LightCo. We will assume that T has an Exponential distribution with a mean, 30,000 hours. The pdf of T is given by:

 

1 f(t) e-y/30000 ,y> 0; 0, otherwise 30000 a. Suppose that I install two of these LED lights to make a double spotlight. Let Tmax represent the time to failure of the last bulb in the pair to burn out. We will assume that the times to failure are independent. For this random variable, Tmax, determine the cdf, Fmax(t), and using the cdf, determine fmax(t), the pdf. [5] b. Now, let Tmin represent the time to failure of the first bulb in the pair to burn out. Again, we will assume that the times to failure are independent. For this random variable, Tmin, determine the cdf, Fmin(t), and using the cdf, determine fmin(t), the pdf. [5] C. Find E(Tmin) and E(Tmax). [4]