An avionics system 'A' is implemented "triple-redundant. Another avionics system 'B' that is dependent on the output of system A uses a method called "mid-value select" to determine which value of the three (redundant) inputs it is going to use. Mid-value select will choose that value of the three inputs that falls in between the two other values, for example, if the inputs are 1.2, 6.7, and 4.5 it chooses 4.5 as its input. Assume that the three threads of system A output: A = 0+w A2 = 0+w2 Az = 0+w where w; is a random variable normally distributed with a mean of zero and a variance of 6. a) Given that 0= 4 what is the probability that the input to system 'B' (after the mid-value select operation) exceeds 10? Show you work! b) If, instead of using mid-value select, system 'B' just takes the average of the three inputs, what is the probability that the averaged input exceeds 10? An avionics system 'A' is implemented "triple-redundant. Another avionics system 'B' that is dependent on the output of system A uses a method called "mid-value select" to determine which value of the three (redundant) inputs it is going to use. Mid-value select will choose that value of the three inputs that falls in between the two other values, for example, if the inputs are 1.2, 6.7, and 4.5 it chooses 4.5 as its input. Assume that the three threads of system A output: A = 0+w A2 = 0+w2 Az = 0+w where w; is a random variable normally distributed with a mean of zero and a variance of 6. a) Given that 0= 4 what is the probability that the input to system 'B' (after the mid-value select operation) exceeds 10? Show you work! b) If, instead of using mid-value select, system 'B' just takes the average of the three inputs, what is the probability that the averaged input exceeds 10