Test: Theory of Random Variable & Noise - Electronics and Communication Engineering (ECE) MCQ

Since 
Now, 

Also,


Hence, option (c) is not correct.

Noise figure,

Since the area under the probability density function is equal to 1, therefore.

or, 
or, 

• The flicker noise occurs at low operating frequencies (few KHz). Hence, statement-1 is not correct.
• The thermal noise voltage is given by,
  Hence, it is proportional to temperature, bandwidth and the value of resistance. Thus, statement-3 is not correct.
• Statements 1 and 4 are correct.

BCC with different probabilities:

According to question,

Here,  P(Y₀/X₀) =  Probability of error when ‘1 ’ is transmitted
P(Y₁/X₀) = Probability of error when ‘0 ’ is transmitted
∴ Probability of error in channel

or, P(E) = 0.604 x 10^-4

The electronic components generate thermal, shot noise. The thermal noise is also called Johnson noise.

The joint CDF (cumulative distribution function ) is
 which will be equal to 1 because the probability of  covers all the possible values of random variables X and Y.
∴ 
According to the definition of CDF, we have

Substituting the value of PDF, we have:

or, 
or, 
or, 
or, 

From above figure we can conclude that both assertion and reason are true and reason is the correct explanation of assertion.

• The conditional PDF is basically a PDF Since i.e. the conditional PDF is a non ­negative function.
Hence, statements 1 and 2 are correct.
 th e area under a conditional PDF is always equal to 1. Hence, statement-3 is also correct.
• If the random variables x and y are statistically independent, then 
This means that the conditional density functions reduce to the marginal density functions. Hence, statement-4 is also correct.

The distribution function of a random variable is the probability that the value taken by the random variable is less than or equal to the real number x.