- #1
aegea
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Many thanks in advance
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!
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!