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Please help me with the below question needed with a clear step by step explanation, please

NEEDED ALL PARTS PLEASE

1. Let X1 and X2 be independent normal random variables with mean 9'. and standard deviation ". Dene Y1 = X1 +X2 and Y2 = X1 -X2. (a) 'What are the distributions of V1 and Y2? (h) Find the joint probabilityr density of Y1 and Y1, and use it to conclude that Y1 and Y: are independent. {o} Now thin]; of'X1 and X: as a random sample of size n = 2 from a normal population. Let X and .52 he the sample mean and variance, respectively. Write X and .52 in terms of 1'1 and V2... and conclude that X and .52 are independent