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Q#1 Random Variable and Random Process GATE EC 2025 MCQ +2 marks -0.66 marks

Consider a real-valued random process

 

where  and  is a positive integer. Here,  for  and 0 otherwise. The coefficients  are pairwise independent, zero-mean unit variance random variables.

Read the following statements about the random process and choose the correct option.

(i) The mean of the process  is independent of time .

(ii) The autocorrelation function  is independent of time  for all .

(Here,  is the expectation operation.)

(i) is TRUE and (ii) is FALSE

Both (i) and (ii) are TRUE

Both (i) and (ii) are FALSE

(i) is FALSE and (ii) is TRUE

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