You visited us 7 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Energy of a Capacitor

A stationary ...

Question

A stationary random process X(t) is applied to the circuit shown below:

If the mean value of the input process X(t) is 5, then the mean value of the output process Y(t) will be

No worries! We‘ve got your back. Try BYJU‘S free classes today!

0.8

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

Open in App

Solution

The correct option is D 4
$E [X (t)] = 5$

$E [Y (t)] = H (0) E [X (t)]$

$H (0) H (s)_{s = 0}$

H(s)= Transfer funciton of the given circuit

From the given circuit,
$H (0) = \frac{4 M Ω}{4 M Ω + 1 M Ω} = \frac{4}{5} = 0.80$

$So, [Y (t)] = 0.80 \times 5 = 4$

Suggest Corrections

Similar questions

Q. For the system shown in the figure below, the input

X (t)

is a stationary random process.

If the statistical mean value of the input process X(t) is 8, then the statistical mean value of the output process Y(t) will be ________

Q. A stationary random process X(t) is applied to an LTI system whose impilse response is

h (t) = e^{- 2 t^{2}}

The output process of this LTI system is Y(t). If the mean value of the process X(t) is 2, then the mean value of the process Y(t) will be ______

Q. Consider a random process

Y (t)

defined as

Y (t) = X (t) - X (t + τ)

where

X (t)

is stationary non-periodic process and

^{'} τ^{'}

is constant. If

R_{X} (τ)

is the autocorrelation of random process

X (t)

, then the variance of

Y (t)

will be

Q. For a stationary ergodic process

X (t),

the autocorrelation function

R_{X} (τ)

is given by,

R_{X} (τ) = \frac{τ^{2}}{2 + 9 τ^{2}}

The magnitude of the mean value of

X (t)

i.e.,

| ¯ ¯¯¯ ¯ X |

is ______

X (t)

is a

W S S

random process with an average power of

2 W

, another random process

Y (t)

is defined as,

Y (t) = X (t) c o s (ω_{o} t + θ)

Where,

θ

is a random variable which is uniformly distributed in the interval

[0, 2 π]

and

ω_{0}

is a constant. If

X (t)

and

θ

are statistically independent, then the average power of the random process

Y (t)

will be

Join BYJU'S Learning Program

A stationary random process X(t) is applied to the circuit shown below: If the mean value of the input process X(t) is 5, then the mean value of the output process Y(t) will be

The correct option is D 4E[X(t)]=5 E[Y(t)]=H(0)E[X(t)] H(0)H(s)s=0 H(s)= Transfer funciton of the given circuit From the given circuit, H(0)=4MΩ4MΩ+1MΩ=45=0.80 So, [Y(t)]=0.80×5=4

A stationary random process X(t) is applied to the circuit shown below:

If the mean value of the input process X(t) is 5, then the mean value of the output process Y(t) will be

The correct option is D 4
$E [X (t)] = 5$

$E [Y (t)] = H (0) E [X (t)]$

$H (0) H (s)_{s = 0}$

H(s)= Transfer funciton of the given circuit

From the given circuit,
$H (0) = \frac{4 M Ω}{4 M Ω + 1 M Ω} = \frac{4}{5} = 0.80$

$So, [Y (t)] = 0.80 \times 5 = 4$