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aegea

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Suppose x is normal variable x~N(a,b)

and y=160*x^2

I need calculate E(y)=∫yf(y)d(y)

f(y) is the density function of y

how can I write it as an integral of x since we know x's distribution, I mean use the density function of x to substitute the original integral

Can I just use E(y)=E(160 x^2)= ∫ 160 x^2 f(x) d(x)

then I can use f(x), which is the density function of normal.

Seems right, but seems wrong, seems I use f(x) to substitute x directly!