In Minecraft, TNT produces rectangular craters when it blows up. It is known that the length L (in metres) and width W (in metres) of the rectangle are discrete random variables with joint probability function f(l, w) = klw², for w = 1,2, l = 1,2, 3, where k is a positive constant. Find the value of k. Determine and justify if L and W are independent. Find the conditional probability function of W given L = 2. Let A be the area of the rectangle formed, A = L ×W. Find the range and probability function of A.

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