The probability density function of a signal x[ t] is given

The probability density function of a signal x[ t] is given by
P_x(x) = 1 |x|. e^{– |x|}
2

the probability that x > 1 is—

P(x > 1) =		^∞	P_x(x).dx =		^∞	\|x\|	e^–\|x\|dx
		₁			₁	2

=		^∞	\|x\|	e^–xdx
		₁	2

^∞

e^–xdx –

^∞

e^–xdx

₁

=	1		x^-x	+		^∞	e^-x	dx
	2		- 1			₁	1

=	1	[– xe^–x – e^–x]^∞₁
	2

= 1/e = 0·368

P_x(x) =	1	\|x\|. e^{– \|x\|}
	2