The density function of a random variable X is given by: f(x)={(cx , 0<X<2 0 otherwise)┤ The S.D
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total answers (1)
Mathematics
Since ∫_(-∞)^∞ 〖f(x)〗 dx=1
need an explanation for this answer? contact us directly to get an explanation for this answer∴1=c∫_0^2 x dx=c/2 [x^2 ]_0^2=2c→c=1/2
E(X)=1/2 ∫_0^2 x^2 dx=1/2 [x^3/3]_0^2=4/3
E(X^2 )=1/2 ∫_0^2 x^3 dx=1/2 [x^4/4]_0^2=2
∴E(3X^2-2X)=3E(X^2 )-2E(X)=6-8/3=10/3
V(X)=E(X^2 )-(E(X) ) ̅ ́^2=2-16/9=2/9
∴σ_x=√(V(X))=√2/3