Consider Exercise 4.11 from the textbook. In this exercise, let XA be the lifetime of block A, XB be the lifetime of block B, and T be the lifetime of the satellite. The lifetimes are in years. It is given that XA and XB follow independent exponential distributions with mean 10 years. One can follow the solution of Exercise 4.6 to show that the probability density function of T is fT (t) = ( 0.2 exp(0.1t) 0.2 exp(0.2t), 0 t < , 0, otherwise, and E(T) = 15 years. (a) Use the above density function to analytically compute the probability that the lifetime of the satellite exceeds 15 years. (b) Use the following steps to take a Monte Carlo approach to compute E(T) and P(T > 15). i. Simulate one draw of the block lifetimes XA and XB. Use these draws to simulate one draw of the satellite lifetime T. ii. Repeat the previous step 1000 times. This will give you 1000 draws from the distribution of T. iii. Make a histogram of the draws of T using 'hist' function. Superimpose the density function given above. Try using the 'curve' function for drawing the density. Note what you