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Let X be a random variable whose density is given by the formula
f(x) = cx² if x ∈ (0, 2)
0 if otherwise.
(a) Find c.
(b) Let Y be the integer part of X, i.e., Y = 0 if 0 ≤ X < 1 and Y = 1 if 1 ≤ X < 2. Let Z be the fractional part of X, i.e., Z = X −Y . Find the correlation between Y and Z.

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Let X be a random variable whose density is given by the formula f(x) = cx2 if x ∈ (0, 2) 0 if otherwise. (a) Find c.