Homework Sourse4 10 The density for a random variable X is given by fx3x 4
4. [10] The density for a random variable X is given by f(x)=3x^ - 4 1 ![4. [10] The density for a random variable X is given by f(x)=3x^ - 4 1 SolutionE[x^2] = (int -inf to inf) ( f(x)*x^2 )dx = (int 1 to inf) (x^2 * 3x^-4) dx = (i](/WebImages/9/4-10-the-density-for-a-random-variable-x-is-given-by-fx3x-4-998969-1761514398-0.webp "4. [10] The density for a random variable X is given by f(x)=3x^ - 4 1 SolutionE[x^2] = (int -inf to inf) ( f(x)*x^2 )dx = (int 1 to inf) (x^2 * 3x^-4) dx = (i")
Solution
E[x^2] = (int -inf to inf) ( f(x)*x^2 )dx
= (int 1 to inf) (x^2 * 3x^-4) dx
= (int 1 to inf) (3x^-2) dx
= (-3/x) (lim 1 to inf)
= 0 - (-3)
= 3
so,
E[x^2] = 3
Var[x] = E[x^2] - (E[x])^2 = 3 - (3/2)^2 = 3 - 9/4 = 3/4
