Let X be a r.v. has a p.d.f f(x) given by: f(x)={(4/π(1+x^2 ) , 0≤X≤1 0 otherwise)┤ Evaluate E(X)
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Mathematics
∵E(X)=∫_(-∞)^∞ 〖xf(x)〗 dx
need an explanation for this answer? contact us directly to get an explanation for this answer∴E(X)=∫_0^1〖4x/(π(1+x^2)) dx〗=4/π ∫_0^1 xdx/(1+x^2 )=2/π [ln(1+x^2 ) ]_0^1=2/π ln2