Homework SourseLet X have the density fx for 0 Solutiona EX Integralx fx
Let X have the density f(x) = for 0 ![Let X have the density f(x) = for 0 Solutiona) EX = Integral[x f(x) dx] = Integral [x (3/8)x^2 dx]|(0,2) = (3/8) x^4/4|(0,2) = 1.5 [ANSWER] **************** b)](/WebImages/3/let-x-have-the-density-fx-for-0-solutiona-ex-integralx-fx-969607-1761499372-0.webp "Let X have the density f(x) = for 0 Solutiona) EX = Integral[x f(x) dx] = Integral [x (3/8)x^2 dx]|(0,2) = (3/8) x^4/4|(0,2) = 1.5 [ANSWER] **************** b)")
Solution
a)
EX = Integral[x f(x) dx]
= Integral [x (3/8)x^2 dx]|(0,2)
= (3/8) x^4/4|(0,2)
= 1.5 [ANSWER]
****************
b)
EX^2 = Integral[x^2 f(x) dx]
= Integral [x^2 (3/8)x^2 dx]|(0,2)
= (3/8) x^5/5|(0,2)
= 2.4 [ANSWER]
*********************
c)
EX^k = Integral[x^k f(x) dx]
= Integral [x^k (3/8)x^2 dx]|(0,2)
= (3/8) [x^(k+3)]/(k+3)|(0,2)
= (3/8) [2^(k+3)]/(k+3)|(0,2)
or, as 8 = 2^3,
EX^k = 3(2^k)/(k+3) [ANSWER]
