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What are some toy models I can use in R?

Do you mean you have data from N(5,2) that has had data from N(3,1) added to it, or that you have two different sets of data?
Or do you mean that you want to know how to generate such data?
If you generate random data correctly following a model, the model will indeed predict the data pretty well. But under those circumstances it seems redundant to ask the question. Were you thinking of fitting a (possibly different) model to the data at some point ?  If so, what model would you want to fit? And what would you want to predict from it?
What parameters do you want to estimate?
Unclear on that at present. See above.


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