Suppose that fx 15x2 for 1 SolutionIntegrating fx Integralf

Suppose that f(x) = 1.5x^2 for -1

Solution

Integrating f(x),

Integral[f(X) dx] = 1.5x^3 / 3 = 0.5x^3, -1<x<1

and 0 otherwise.

a)

P(X>0) = 0.5(1^3) - 0.5(0^3) = 0.5 [answer]

************

b)

P(X>0.5) = 0.5(1^3) - 0.5(0.5^3) = 0.4375 [answer]

***************

c)

P(-0.5<x<0.5) = 0.5(0.5)^3 - 0.5[(-0.5)^3] = 0.125 [answer]

****************

d)

P(X < -2) = 0, [answer]

as f(x) = 0 for x < -1.

******************

Hi! Please submit the next part as a separate question. That way we can continue helping you! Thanks!