1. Probability function when output Z(t) related to input y(t) as Y = √Z, and probability density function of input
   

   p(y) =		e– y; 0 < y < ∞
   		0; – ∞ < y < 0

1. 1. 2√z e^{– √z}

   
   
   

   2. – e√z

      2√z

   
   
   

   3. e^{– z}

   
   
   

   4. e^z

   
   
   

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1. View Hint View Answer Discuss in Forum

   Let Y = √2 z = g(y)
   

   g′(y) =	1	z–1/2 =	1
   	2		2√z

   
   

   fz(z) =	fy(y)				=	e-y					= 2√ze- √z
   	g′(y)					1
   						2√y

   Correct Option: A

   Let Y = √2 z = g(y)
   

   g′(y) =	1	z–1/2 =	1
   	2		2√z

   
   

   fz(z) =	fy(y)				=	e-y					= 2√ze- √z
   	g′(y)					1
   						2√y

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2. A periodic voltage having the Fourier series V(t) = 1 + 4 sin ωt + 2cos ωt volts is applied across a one-ohm resistor. The power dissipated in 1-ohm resistor is—

1. 1. 1W

   
   
   

   2. 11W

   
   
   

   3. 21W

   
   
   

   4. 24.5W

   
   
   

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1. View Hint View Answer Discuss in Forum

   V_rms of the given Fourier series
   = √1 + 4².½ + 2². ½
   = √11
   Power dissipated in 1 – Ω resistor
   

   =	V2rms	=	(√11)	= 11watt
   	R		1

   Correct Option: B

   V_rms of the given Fourier series
   = √1 + 4².½ + 2². ½
   = √11
   Power dissipated in 1 – Ω resistor
   

   =	V2rms	=	(√11)	= 11watt
   	R		1

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