1. Let X be a continuous random variable with probability density function: f(x) = { 3/4 for 0 ? x ? 1 1/4 for 2 ? x ? 3 0 otherwise. (a) Determine the cumulative distribution function F(x) = P(X ? x). (b) Graph f(x) and F(x). (c) Determine the expected value of X: E[X]. (d) Determine the variance of X: V(X) = E[X²] - E[X]².
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