10. If X is a uniform distribution on [0, 2], determine the distribution (CDF and density) of Y = $X^3$.
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This can be expressed as P(Y ≤ y). Since Y = X^3, we can rewrite this as P(X^3 ≤ y). Since X is uniformly distributed on [0, 2], we can find the CDF of Y by finding the CDF of X and then substituting X^3 for X. The CDF of X is given by: F_X(x) = (x - 0) / (2 - Show more…
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