An electronic system has each of two different types of components in joint operation. Let X and Y denote the lengths of life, in hundreds of hours, for components of type I and type II, respectively. The performance of a component is independent for each other. Let E(X) = 4, E(Y) = 2, E(X2) = 24, E(Y2) = 8. The cost of replacing the two components depends upon their length of life at failure and it is given by C = 50 + 2X + 4Y.
(i) Compute the average cost of replacing the two components. Your final answer must be a number.
(ii) Compute the standard deviation of cost of replacing the two components. Your final answer must be a number.

a

The average cost is

b

The standard deviation of  cost is  

Step-by-step explanation:

From the question we are told that

The cost of replacing the two component is  C =  50 + 2 X + 4 Y

The variance   of X is mathematically represented as

           V(X) =  

Substituting values  

The variance  of Y is mathematically represented as

           V(Y) =  

Substituting values  

The average of  replacing the two component is  

substituting value

The variance  of replacing the two component is  

             Note: The variance of constant is zero

                                                                  and X and  Y are independent  

=>      

substituting values

=>              

=>        

=>        

The standard deviation is

substituting values

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step-by-step explanation: