Question: A certain random variable X has the probability density function (PDF) given by f (x) - 2, -1 0) A certain random variable X has

A certain random variable X has the probability density function (PDF) given by f (x) - 2, -1 0)

A certain random variable X has the probabil;ity density function (PDF) given by 1 a: and 0 otherwise. (a) Find and sketch the cumulative distribution function (CDF) of X. (b) Find the standard deviation (a) of this random variable. '(c) Determine the probability that Xis within two standard deviations of its mean, given that X is positive, i.e. P (20 X 201 X > 0).

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