Question: Let X be a random variable with a distribution function F for which F(x) = x^4 for 0 x 1. (a) Determine F(x) for x

Let X be a random variable with a distribution function F for which F(x) = x^4 for 0 x 1.

(a) Determine F(x) for x<0 and for x>1.

(b) Does X have a probability mass function? If so, determine it.

(c) Does X have a probability density function? If so, determine it.

(d) Compute P(1/2< X 3/4) without using your answers to parts (b) and (c).

(e) Compute P(1/2< X 3/4) using your answer to parts (b) or (c) (or both).

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