let Y=5X+epsilon

where epsilon ~ N(0,1) and X ~ Unif(-1,1).Assume that X and epsilon are independent.

Find E[Y|X=x].

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- so E(5X)=5X? X has a uniform distribution. why we don't compute expectation of X?
- hepingtan
- Oct 01, 2018 at 12:20am

- That would be E(E(Y|X=x))....Which is unconditional expectation..Here we are asked to compute the conditional distribution..Which means I have the knowlendge that X=x....Now I want to compute the expected value of Y given this information
- nabaneetdas
- Oct 01, 2018 at 4:34am

- And by the way, E(5X) is not 5X... E(5X)=0 when X has Unif(-1,1) distribution
- nabaneetdas
- Oct 01, 2018 at 4:35am