Question: I have a normal distribution of BP samples X which is normal distribution with unknow Mu and unknown Sigma. Now the sample has been tempered

I have a normal distribution of BP samples X which is normal distribution with unknow Mu and unknown Sigma. Now the sample has been tempered by adding +1 and substracting -1 with 0.5-0.5 probability . so the final distribution is Z=X[normal distribution] +/-[1] to all elements of X. Now how should I get the maximum likelihood of Z ...the final distribution with X and +/- 1 to all samples of X.

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