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## Homework Statement

A piece of laminated plywood consists of 3 pieces of wood of type A and 2 pieces of type B. The thickness of type A has a mean 2mm and variance 0.04mm

^{2}and The thickness of type B has a mean 1mm and variance 0.01mm

^{2}. Find the mean and variance of the thickness of the laminated plywood.

## Homework Equations

E(aX + bY) = aE(X) + bE(Y)

Var(aX + bY) = a

^{2}Var(X) + b

^{2}Var(Y)

## The Attempt at a Solution

so T = 3A + 2B

E(T) = 3E(A) + 2E(B) = 8mm (This is correct)

**Now :**Var(T) = 3

^{2}Var(A) + 2

^{2}Var(B)

=9*0.04 + 4*0.01 = 0.36+0.04 = 0.4 (Which is wrong.... according to the book the answer should be

**0.14mm**

^{2})

How? What am I doing wrong?