and Var(aX+b)a Var(X) 2.6.3 Suppose that Xi, X2, and X3 are independent random v

Question

and Var(aX+b)a Var(X) 2.6.3 Suppose that Xi, X2, and X3 are independent random variables each with a mean of and a variance of 2. Compare the means and variances of Y=3X1 and Z=X1 + X2 + X3 2.6.4 A machine part is assembled by fastening two components of type A and one component of type B end to end. Suppose that the lengths of components of type A have an expectation of 37.0 mm and a standard deviation of 0.7 mm, whereas the lengths of components of type B have an expectation of 24.0 mm and a standard deviation of 0.3 mm. What are the expectation and variance of the length of the machine part?

Explanation / Answer

Let Type A

E(A) = 37mm

V(A) = 0.72 = 0.49

Let Type B

E(B) = 24

V(B) = 0.32 = 0.09

Machine part is assembled by 2 components of type A and 1 component of type B.

Let X be the length of machine part

X =2A + B

E(X) = 2E(A)+E(B) = 2*37+ 24 = 74+24 = 98 mm

V(X) = 4V(A)+ V(B) = 4*0.49+ 0.09 = 1.96+0.09 =2.05

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