Let X be a continuous random variable defined on the interval [0, 4] with probability density function: p(x) = c(1 + 4x) (a) Find the value of c such that p(x) is a valid probability density function. (b) Find the probability that X is greater than 3. (c) If X is greater than 1, find the probability X is greater than 2. Also find the probability that X is less than some number a, assuming 0 < a < 4?

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