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A random process is defined by X(t) + A where A is continuous random variable uniformly distributed on (0,1). The auto correlation function and mean of the process is
  • a)
    1/2 & 1/3
  • b)
    1/3 & 1/2
  • c)
    1 & 1/2
  • d)
    1/2 & 1
Correct answer is option 'B'. Can you explain this answer?
Most Upvoted Answer
A random process is defined by X(t) + A where A is continuous random v...
The autocorrelation function of a random process can be defined as:

R_X(t1, t2) = E[X(t1) * X(t2)]

Since X(t) = A for all t, we can substitute X(t) with A in the above equation:

R_X(t1, t2) = E[A(t1) * A(t2)]

Since A is uniformly distributed on (0,1), its mean is 1/2. We can substitute this into the autocorrelation function:

R_X(t1, t2) = E[A(t1) * A(t2)] = 1/2 * 1/2 = 1/4

Therefore, the autocorrelation function of the random process is 1/4.

The mean of the process can be calculated as:

E[X(t)] = E[A] = 1/2

Therefore, the mean of the random process is 1/2.
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Community Answer
A random process is defined by X(t) + A where A is continuous random v...
E[X(t)X(t + t)] = 1/3 and E[X(t)] = 1/2 respectively.
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A random process is defined by X(t) + A where A is continuous random variable uniformly distributed on (0,1). The auto correlation function and mean of the process isa)1/2 & 1/3b)1/3 & 1/2c)1 & 1/2d)1/2 & 1Correct answer is option 'B'. Can you explain this answer?
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