Question: Consider the function defined by p(x) = 2 2x 0 x < 1 0 otherwise. (a) Sketch p(x). (b) Is p(x) a valid

Consider the function defined by p(x) =

2 − 2x 0 ≤ x < 1 0 otherwise.

(a) Sketch p(x).

(b) Is p(x) a valid probability density function? Why or why not?

(c) What is the probability that x ≥ 1/2?

(d) What is the probability that x = 1/2?

(e) For very small , what is the probability that x is within of 1/2?

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