(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

X_{1}∼ N(μ_{1},σ_{1}^{2}) and X_{2}∼ N(μ_{2},σ_{2}^{2})

Let Y = X_{1}+ X_{2}

Find the p.d.f. of Y & label the distribution.

2. Relevant equations

3. The attempt at a solution

Not quite sure how to go about this problem.

µ_{Y}=E[Y]=E[X_{1}+X_{2}]=E[X_{1}]+E[X_{2}]=µ_{1}+µ_{2}

σ_{Y}^{2}=E[Y^{2}] - µ_{Y}^{2}

E[X_{1}^{2}+ 2X_{1}X_{2}+X_{2}^{2}] - (µ_{1}+µ_{2})^{2}

I think that might be how you start it. Feel free to correct me and start over or continue. Thanks.

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# Find the p.d.f. and identify.

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