Let X be a r.v. has a p.d.f given by: f(x)={(4/π(1+x^2 ) , 0≤X≤1 0 otherwise)┤ Find E(3X+5)
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Mathematics
∵E(X)=∫_(-∞)^∞ x f(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=2/π ∫_0^1 2xdx/(1+x^2 )=[2/π ln(1+x^2 )]_0^1=2/π [ln2 ]=2/π (0.69)=0.44
Note:
E(X^2 )=4/π-1
V(X)=4/π [1-1/π (ln2 )^2 ]-1=0.076 →σ=0.28