the probability density function pdf of x is, Basic Statistics

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the probability density function pdf of x is

The probability density function (pdf) of X is given by

f(x) = (1-x/2 if 0 ≤ x < 2

(0 otherwise

a. Verify that that f(x) is a legitimate pdf.

b. Sketch the graph of the pdf function

c. Find the distribution function of X and sketch the graph.

d) Compute P(1

e) Find the expected value and the variance of X

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