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The (mixed) random variable X has probability density function (pdf) fX (x) given by: fx(x)=0.5δ(x−3)+ { c.(4-x2),...

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Statistics

The (mixed) random variable X has probability density function(pdf) fX (x) given by:

fx(x)=0.5δ(x−3)+ { c.(4-x2), 0≤x≤2

0, otherwise

where c is a constant.

(a) Sketch fX (x) and find the constant c.

(b) Find P (X > 1).

(c) Suppose that somebody tells you {X > 1} occurred. Findthe conditional pdf fX|{X>1}(x), the pdf of X giventhat {X > 1}.

(d) Find FX(x), the cumulative distribution function of X.

(e) Let Y = X2 . Find fY (y), the probability densityfunction of the random variable Y

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