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A continuous random variable has probability density function f(x)=6(x−x)2,0≤x≤i, Find (i) mean (ii) variance.
1 Answer
written 8.7 years ago by |
Mean = E (x)
=∞∫−∞x.f(x).dx
=1∫0x.6(x−x2)dx=61∫0(x2−x3)dx=6[x33−x44]10=6[(133−144)−(0−0)]=0.5ConsiderE(x2)=∞∫−∞x2.f(x)dx=1∫0x2.6(x−x2)dx=61∫0[x3−x4]dx=6[x44−x55]10=6[(144−155)−(0−0)]=0.3
Variance =E(x2)–[E(x)]2=0.3–0.52=0.05
Hence, Mean =0.5 and …