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Assertion (A): if the random process x(t) changes very rapidly with time, the autocorrelation function will decrease rapidly to zero.
Reason (R): The autocorrelation function Rx(τ) is a measure of interdependence of two random variables obtained by observing the random process x(t) at time τ seconds apart.
  • a)
    Both A and R are true and R is the correct explanation of A.
  • b)
    Both A and R are true but R is not the correct explanation of A,
  • c)
    A is true but R is false.
  • d)
    A is false but R is true.
Correct answer is option 'A'. Can you explain this answer?
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Assertion (A): if the random process x(t)changes very rapidly with tim...

From above figure we can conclude that both assertion and reason are true and reason is the correct explanation of assertion.
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Assertion (A): if the random process x(t)changes very rapidly with tim...
Understanding the Assertion and Reason
The assertion (A) states that if a random process x(t) changes very rapidly with time, its autocorrelation function will decrease rapidly to zero. The reason (R) explains that the autocorrelation function Rx(τ) measures the interdependence of two random variables observed at a time τ seconds apart.
Explanation of Assertion (A)
- A random process that changes rapidly tends to have values that are less correlated with their past values.
- When the process varies quickly, the values at different time instances become less similar, leading to a rapid decrease in the autocorrelation function.
- This phenomenon reflects a lower degree of predictability for the process as time intervals increase, resulting in Rx(τ) approaching zero more swiftly.
Analysis of Reason (R)
- The reason accurately describes the nature of the autocorrelation function as a statistical tool that assesses the relationship between values of the process at different times.
- However, it does not directly explain why the rapid changes in the process lead to a quick decline in the autocorrelation function.
Correctness of Both Statements
- Both A and R are true: A is correct in stating the behavior of the autocorrelation function, while R accurately defines what the function represents.
- However, R does not provide a direct explanation for A’s assertion; hence, it is not the correct explanation.
Conclusion
- The correct answer is option (a): Both A and R are true, but R is not the correct explanation of A.
- Understanding these concepts is essential in analyzing stochastic processes in the field of Electronics and Communication Engineering.
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Assertion (A): if the random process x(t)changes very rapidly with time, the autocorrelation function will decrease rapidly to zero.Reason (R): The autocorrelation function Rx(τ) is a measure of interdependence of two random variables obtained by observing the random process x(t) at time τ seconds apart.a)Both A and R are true and R is the correct explanation of A.b)Both A and R are true but R is not the correct explanation of A,c)A is true but R is false.d)A is false but R is true.Correct answer is option 'A'. Can you explain this answer?
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