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So I calculate the E[X] as equal to p_1*mean_1 p_2*mean_2. And then E[Y] would be w_1*E[X] E[ϵ], which would be also 0 because E[X] = 0 and E[ϵ] will be 0 as the mean is 0 for this gaussian distribution as defined above in the problem.
So based on these two E[XY] would be 0 i'm having a fair bit of trouble with mathematical proofs and this question has me stumped, I've tried going through direct and indirect proofs and just can't quite grasp the concepts I have to apply... Hi, I'm Brendan and I've recently started focusing more on my You Tube Channel Cusack Prep.
Now, let's consider a concrete example when m=2, p_1=p_2=0.5, w_1=1,w_2=−1, μ_1=2, μ_2=−2, and σ_1=σ_2=1, what is the value of E[X], E[Y], E[XY]?
My approach was that for E[X] each distribution's expected value would be equal to its mean (integrating a gaussian distribution from -infinity to infinity).
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