If the probability density function of a continuous random variable X is `f(x)={{:((3+2x)/(18),2lexle4),(0,x2" or"xgt4):}` Then the mathematical expectation of X isA. `(83)/(27)`B. `(27)/(83)`C. `(87)/(23)`D. `(38)/(72)`

If the probability density function of a continuous random variable X

1.	If the probability density function of a continuous random variable X is `f(x)={{:((3+2x)/(18),2lexle4),(0,x2" or"xgt4):}` Then the mathematical expectation of X isA. `(83)/(27)`B. `(27)/(83)`C. `(87)/(23)`D. `(38)/(72)`
Answer» Correct Answer - A `E(X)=oversetoounderset(-oo)intxf(x)dx=0+overset4underset2intx((3+2x)/(18))dx+0` `=1/(18)overset4underset2int(3x+2x^2)dx=1/(18)[(3x^2)/2+(2x^3)/3]_2^4` `=1/(18)[(24+(128)/3)-(6+(16)/3)]=1/(18)xx(166)/3=(83)/(27)`

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If the probability density function of a continuous random variable X is `f(x)={{:((3+2x)/(18),2lexle4),(0,x2" or"xgt4):}` Then the mathematical expectation of X isA. `(83)/(27)`B. `(27)/(83)`C. `(87)/(23)`D. `(38)/(72)`

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