Question: Xis a continuous random variable. The probability density function (PDF) ofXis fX(x)=?1/2e^?x,x?0;fX(x)=1/2e^x,x (a) ShowfX(x) is a valid PDF. (b) Given a positive numbert, find the

Xis a continuous random variable. The probability density function (PDF) ofXis

fX(x)=?1/2e^?x,x?0;fX(x)=1/2e^x,x

(a) ShowfX(x) is a valid PDF.

(b) Given a positive numbert, find the probabilityP(|X| ?t).

(c) Find the probability of|X| ?1, given|X| ?2, that isP({|X| ?1}|{|X| ?2})

(d) Write down thecumulativedistribution function (CDF) ofX.

Xis a continuous random variable. The probability density function (PDF) ofXisfX(x)=?1/2e^?x,x?0;fX(x)=1/2e^x,x(a) ShowfX(x)

X is a continuous random variable. The probability density function (PDF) of X is fx (2) e- , x 2 0; ,

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